{"id":13498,"date":"2025-06-02T19:10:08","date_gmt":"2025-06-02T12:10:08","guid":{"rendered":"https:\/\/www.ckconitsha.com\/vn\/?p=13498"},"modified":"2025-07-02T15:15:04","modified_gmt":"2025-07-02T08:15:04","slug":"chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap","status":"publish","type":"post","link":"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/","title":{"rendered":"Chuy\u00ean \u0111\u1ec1 s\u1ed1 ph\u1ee9c \u00f4n thi THPT Qu\u1ed1c Gia m\u00f4n To\u00e1n: L\u00fd thuy\u1ebft &amp; B\u00e0i t\u1eadp"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#So_phuc_trong_cau_truc\" >S\u1ed1 ph\u1ee9c trong c\u1ea5u tr\u00fac<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Kien_thuc_chung_ve_chu_de_kiem_tra_truong_trung_hoc_quoc_gia\" >Ki\u1ebfn th\u1ee9c chung v\u1ec1 ch\u1ee7 \u0111\u1ec1 ki\u1ec3m tra tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Khai_niem_ve_cac_so_phuc_tap\" >Kh\u00e1i ni\u1ec7m v\u1ec1 c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Hai_so_phuc_tap_bang_nhau\" >Hai s\u1ed1 ph\u1ee9c t\u1ea1p b\u1eb1ng nhau<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Hieu_suat_hinh_hoc_cua_cac_so_phuc_tap\" >Hi\u1ec7u su\u1ea5t h\u00ecnh h\u1ecdc c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Bo_sung_va_tru_cac_so_phuc_tap\" >B\u1ed5 sung v\u00e0 tr\u1eeb c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Phep_nhan_phuc_tap\" >Ph\u00e9p nh\u00e2n ph\u1ee9c t\u1ea1p<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#So_phuc\" >S\u1ed1 ph\u1ee9c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Mo_-dun_cua_cac_so_phuc\" >M\u00f4 -\u0111un c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#So_luong_so_luong_phuc_tap_khac_voi_0\" >S\u1ed1 l\u01b0\u1ee3ng s\u1ed1 l\u01b0\u1ee3ng ph\u1ee9c t\u1ea1p kh\u00e1c v\u1edbi 0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Phuong_trinh_bac_hai_voi_he_so_thuc\" >Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai v\u1edbi h\u1ec7 s\u1ed1 th\u1ef1c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Mot_so_ket_qua_nhanh_chong_cua_cac_so_phuc_tap_can_nho\" >M\u1ed9t s\u1ed1 k\u1ebft qu\u1ea3 nhanh ch\u00f3ng c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p c\u1ea7n nh\u1edb<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Huong_dan_ve_cach_giai_quyet_cac_hinh_thuc_cua_cac_bai_tap_phuc_tap_cua_truong_trung_hoc_quoc_gia\" >H\u01b0\u1edbng d\u1eabn v\u1ec1 c\u00e1ch gi\u1ea3i quy\u1ebft c\u00e1c h\u00ecnh th\u1ee9c c\u1ee7a c\u00e1c b\u00e0i t\u1eadp ph\u1ee9c t\u1ea1p c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Mau_1_Tinh_cac_phan_tu_cua_so_phuc\" >M\u1eabu 1: T\u00ednh c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a s\u1ed1 ph\u1ee9c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Mau_2_Phuong_trinh_tren_tap_hop_phuc\" >M\u1eabu 2: Ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean t\u1eadp h\u1ee3p ph\u1ee9c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Mau_3_Tim_so_phuc_de_dap_ung_cac_dieu_kien\" >M\u1eabu 3: T\u00ecm s\u1ed1 ph\u1ee9c \u0111\u1ec3 \u0111\u00e1p \u1ee9ng c\u00e1c \u0111i\u1ec1u ki\u1ec7n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Mau_4_Bieu_dien_hinh_hoc_cua_cac_so_phuc\" >M\u1eabu 4: Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.ckconitsha.com\/vn\/chuyen-de-so-phuc-on-thi-thpt-quoc-gia-mon-toan-ly-thuyet-bai-tap\/#Mau_5_Toi_uu_cua_so_phuc\" >M\u1eabu 5: T\u1ed1i \u01b0u c\u1ee7a s\u1ed1 ph\u1ee9c<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<\/p>\n<p>B\u1ea1n \u0111ang \u0111\u1ea5u tranh \u0111\u1ec3 xem x\u00e9t k\u1ef3 thi to\u00e1n c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia, \u0111\u1eb7c bi\u1ec7t l\u00e0 ch\u1ee7 \u0111\u1ec1 s\u1ed1 ph\u1ee9c. \u0110\u1eebng lo l\u1eafng! T\u00f3m t\u1eaft ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p (l\u00fd thuy\u1ebft v\u00e0 b\u00e0i t\u1eadp) m\u00e0 kh\u1ec9 cung c\u1ea5p trong b\u00e0i vi\u1ebft n\u00e0y s\u1ebd l\u00e0 ng\u01b0\u1eddi b\u1ea1n \u0111\u1ed3ng h\u00e0nh m\u1ea1nh m\u1ebd \u0111\u1ec3 gi\u00fap b\u1ea1n chinh ph\u1ee5c \u0111i\u1ec3m cao trong k\u1ef3 thi s\u1eafp t\u1edbi.<\/p>\n<p>                        Xem t\u1ea5t c\u1ea3<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"So_phuc_trong_cau_truc\"><\/span>S\u1ed1 ph\u1ee9c trong c\u1ea5u tr\u00fac<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">D\u1ef1a tr\u00ean c\u00e1c c\u00e2u h\u1ecfi thi do B\u1ed9 Gi\u00e1o d\u1ee5c v\u00e0 \u0110\u00e0o t\u1ea1o xu\u1ea5t b\u1ea3n, trong c\u1ea5u tr\u00fac c\u1ee7a b\u00e0i ki\u1ec3m tra to\u00e1n trung h\u1ecdc qu\u1ed1c gia n\u0103m 2024, ch\u1ee7 \u0111\u1ec1 s\u1ed1 ph\u1ee9c t\u1ea1p chi\u1ebfm kho\u1ea3ng 6 c\u00e2u h\u1ecfi, bao g\u1ed3m 4 c\u00e2u trong tr\u00ecnh \u0111\u1ed9 nh\u1eadn th\u1ee9c v\u00e0 hi\u1ec3u bi\u1ebft, 2 c\u00e2u c\u00f3 m\u1ee9c \u0111\u1ed9 \u1ee9ng d\u1ee5ng v\u00e0 \u1ee9ng d\u1ee5ng cao. Do \u0111\u00f3, xem x\u00e9t c\u1ea9n th\u1eadn v\u1ec1 ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 c\u00e1c con s\u1ed1 ph\u1ee9c t\u1ea1p l\u00e0 v\u00f4 c\u00f9ng quan tr\u1ecdng \u0111\u1ed1i v\u1edbi c\u00e1c th\u00ed sinh tham gia k\u1ef3 thi c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia n\u0103m 2024.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Kien_thuc_chung_ve_chu_de_kiem_tra_truong_trung_hoc_quoc_gia\"><\/span>Ki\u1ebfn th\u1ee9c chung v\u1ec1 ch\u1ee7 \u0111\u1ec1 ki\u1ec3m tra tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">D\u01b0\u1edbi \u0111\u00e2y l\u00e0 t\u1ea5t c\u1ea3 c\u00e1c ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 nh\u1eefng con s\u1ed1 ph\u1ee9c t\u1ea1p trong k\u1ef3 thi c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia \u0111\u00e3 \u0111\u01b0\u1ee3c kh\u1ec9 t\u00f3m t\u1eaft, gi\u00fap c\u00e1c \u1ee9ng c\u1eed vi\u00ean d\u1ec5 d\u00e0ng xem x\u00e9t h\u01a1n.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Khai_niem_ve_cac_so_phuc_tap\"><\/span>Kh\u00e1i ni\u1ec7m v\u1ec1 c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">C\u00e1c s\u1ed1 ph\u1ee9c l\u00e0 m\u1ed9t bi\u1ec3u th\u1ee9c \u1edf d\u1ea1ng A + Bi, trong \u0111\u00f3 A, B l\u00e0 s\u1ed1 th\u1ef1c v\u00e0 s\u1ed1 I th\u1ecfa m\u00e3n i2 = -1. <\/p>\n<p dir=\"ltr\">Bi\u1ec3u t\u01b0\u1ee3ng s\u1ed1 ph\u1ee9c l\u00e0 z, \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0 z = a + bi.<\/p>\n<p dir=\"ltr\">Trong \u0111\u00f3:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">T\u00f4i \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ed9t \u0111\u01a1n v\u1ecb \u1ea3o<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">A \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u1ea7n th\u1ef1c, bi\u1ec3u t\u01b0\u1ee3ng re (z) = a<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u1ea7n \u1ea3o c\u1ee7a s\u1ed1 ph\u1ee9c z = a + ball, k\u00fd hi\u1ec7u im (z) = b<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u1ed9 s\u01b0u t\u1eadp c\u00e1c s\u1ed1 ph\u1ee9c l\u00e0 C.<\/p>\n<\/li>\n<\/ul>\n<p dir=\"ltr\">Ghi ch\u00fa: <\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">M\u1ed7i s\u1ed1 th\u1ef1c d\u01b0\u01a1ng \u0111\u01b0\u1ee3c coi l\u00e0 m\u1ed9t s\u1ed1 ph\u1ee9c v\u1edbi c\u00e1c ph\u1ea7n \u1ea3o b = 0, z = a.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">S\u1ed1 ph\u1ee9c Z = A + Ball c\u00f3 a = 0 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 s\u1ed1 thu\u1ea7n t\u00fay \u1ea3o ho\u1eb7c s\u1ed1 \u1ea3o.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">S\u1ed1 0 l\u00e0 c\u1ea3 m\u1ed9t s\u1ed1 th\u1ef1c v\u00e0 m\u1ed9t s\u1ed1 \u1ea3o.<\/p>\n<\/li>\n<\/ul>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Hai_so_phuc_tap_bang_nhau\"><\/span>Hai s\u1ed1 ph\u1ee9c t\u1ea1p b\u1eb1ng nhau<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1eb7t z = a + b\u00f3ng v\u00e0 z &#8216;= a&#8217; + b&#8217;i.<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/1-chuyen-de-so-phuc.png\" alt=\"\" width=\"150\" height=\"60\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Hieu_suat_hinh_hoc_cua_cac_so_phuc_tap\"><\/span>Hi\u1ec7u su\u1ea5t h\u00ecnh h\u1ecdc c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">M\u1ed7i s\u1ed1 ph\u1ee9c \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ecb b\u1eb1ng m\u1ed9t \u0111i\u1ec3m m (a; b) tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 oxy.<\/p>\n<p dir=\"ltr\">Ng\u01b0\u1ee3c l\u1ea1i, m\u1ed7i \u0111i\u1ec3m m (a; b) \u0111\u1ea1i di\u1ec7n cho m\u1ed9t s\u1ed1 ph\u1ee9c z = a + bi.<\/p>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/2-chuyen-de-so-phuc.png\" alt=\"Hi\u1ec7u su\u1ea5t h\u00ecnh h\u1ecdc c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c. (\u1ea2nh: B\u1ed9 s\u01b0u t\u1eadp Internet)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Bo_sung_va_tru_cac_so_phuc_tap\"><\/span>B\u1ed5 sung v\u00e0 tr\u1eeb c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Cho hai s\u1ed1 ph\u1ee9c z = a + ball v\u00e0 z &#8216;= a&#8217; + b&#8217;i. <\/p>\n<p dir=\"ltr\">Ngh\u0129a l\u00e0:<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/3-chuyen-de-so-phuc.png\" alt=\"\" width=\"200\" height=\"57\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Phep_nhan_phuc_tap\"><\/span>Ph\u00e9p nh\u00e2n ph\u1ee9c t\u1ea1p<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Cho hai s\u1ed1 ph\u1ee9c z = a + ball v\u00e0 z &#8216;= a&#8217; + b&#8217;i. <\/p>\n<p dir=\"ltr\">Ngh\u0129a l\u00e0:<\/p>\n<p dir=\"ltr\">Zz &#8216;= aa&#8217; &#8211; bb &#8216; + (ab&#8217; &#8211; a&#8217;b) i<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"So_phuc\"><\/span>S\u1ed1 ph\u1ee9c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">C\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p l\u00e0 m\u1ed9t n\u1ed9i dung quan tr\u1ecdng c\u1ee7a s\u1ed1 ph\u1ee9c m\u00e0 c\u00e1c \u1ee9ng c\u1eed vi\u00ean c\u1ea7n l\u01b0u \u00fd.<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/4-chuyen-de-so-phuc.png\" alt=\"\" width=\"666\" height=\"282\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mo_-dun_cua_cac_so_phuc\"><\/span>M\u00f4 -\u0111un c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/5-chuyen-de-so-phuc.png\" alt=\"\" width=\"650\" height=\"131\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"So_luong_so_luong_phuc_tap_khac_voi_0\"><\/span>S\u1ed1 l\u01b0\u1ee3ng s\u1ed1 l\u01b0\u1ee3ng ph\u1ee9c t\u1ea1p kh\u00e1c v\u1edbi 0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Cho s\u1ed1 ph\u1ee9c z = a + bi \u2260 0 (t\u1ee9c l\u00e0 a2 + b2&gt; 0)<\/p>\n<p dir=\"ltr\">Ch\u00fang t\u00f4i x\u00e1c \u0111\u1ecbnh s\u1ed1 ngh\u1ecbch \u0111\u1ea3o Z-1 c\u1ee7a s\u1ed1 ph\u1ee9c Z 0, l\u00e0 s\u1ed1:<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/6-chuyen-de-so-phuc.png\" alt=\"\" width=\"200\" height=\"74\"><\/p>\n<p dir=\"ltr\">Thuong Z &#8216;\/Z c\u1ee7a Ph\u00e2n khu ph\u1ee9c t\u1ea1p Z&#8217; theo s\u1ed1 ph\u1ee9c Z 0 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh nh\u01b0 sau:<\/p>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/7-chuyen-de-so-phuc.png\" alt=\"\" width=\"200\" height=\"94\"><\/p>\n<p dir=\"ltr\">Vi\u1ec7c b\u1ed5 sung, ph\u00e9p tr\u1eeb v\u00e0 ph\u00e9p nh\u00e2n c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p \u1edf tr\u00ean c\u0169ng c\u00f3 \u0111\u1ea7y \u0111\u1ee7 c\u00e1c t\u00ednh ch\u1ea5t giao ho\u00e1n v\u00e0 ph\u00e2n t\u00e1n, k\u1ebft h\u1ee3p nh\u01b0 b\u1ed5 sung, tr\u1eeb, nh\u00e2n v\u00e0 chia chung.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Phuong_trinh_bac_hai_voi_he_so_thuc\"><\/span>Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai v\u1edbi h\u1ec7 s\u1ed1 th\u1ef1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/8-chuyen-de-so-phuc.png\" alt=\"\" width=\"700\" height=\"426\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mot_so_ket_qua_nhanh_chong_cua_cac_so_phuc_tap_can_nho\"><\/span>M\u1ed9t s\u1ed1 k\u1ebft qu\u1ea3 nhanh ch\u00f3ng c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p c\u1ea7n nh\u1edb <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Sau \u0111\u00e2y l\u00e0 m\u1ed9t b\u1ea3n t\u00f3m t\u1eaft ph\u1ee9c t\u1ea1p c\u1ee7a k\u1ef3 thi tuy\u1ec3n sinh \u0111\u1ea1i h\u1ecdc v\u1edbi m\u1ed9t s\u1ed1 k\u1ebft qu\u1ea3 nhanh ch\u00f3ng c\u1ea7n \u0111\u01b0\u1ee3c ghi nh\u1edb, gi\u00fap c\u00e1c \u1ee9ng c\u1eed vi\u00ean gi\u1ea3i quy\u1ebft c\u00e1c c\u00e2u h\u1ecfi nhanh h\u01a1n v\u00e0 d\u1ec5 d\u00e0ng h\u01a1n.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 10pt\">1. I0 = 1 =&gt; I4N = 1<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 10pt\">2. I1 = i =&gt; i4n+1 = i<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 10pt\">3. I2 = -1 =&gt; I4N+2 = -1<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 10pt\">4. I3 = &#8211; i =&gt; i4n+3 = -i<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 10pt\">5. (1 &#8211; i) 2 = -2i<\/p>\n<p>6. (1 + I) 2 = 2i<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Huong_dan_ve_cach_giai_quyet_cac_hinh_thuc_cua_cac_bai_tap_phuc_tap_cua_truong_trung_hoc_quoc_gia\"><\/span>H\u01b0\u1edbng d\u1eabn v\u1ec1 c\u00e1ch gi\u1ea3i quy\u1ebft c\u00e1c h\u00ecnh th\u1ee9c c\u1ee7a c\u00e1c b\u00e0i t\u1eadp ph\u1ee9c t\u1ea1p c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef cung c\u1ea5p h\u01b0\u1edbng d\u1eabn c\u1ee7a c\u00e1c \u1ee9ng c\u1eed vi\u00ean v\u1ec1 c\u00e1ch gi\u1ea3i quy\u1ebft c\u00e1c lo\u1ea1i b\u00e0i t\u1eadp v\u1ec1 s\u1ed1 \u0111\u00e1nh gi\u00e1 b\u00e0i ki\u1ec3m tra tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia theo c\u00e1ch chi ti\u1ebft v\u00e0 nhanh nh\u1ea5t.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_1_Tinh_cac_phan_tu_cua_so_phuc\"><\/span>M\u1eabu 1: T\u00ednh c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a s\u1ed1 ph\u1ee9c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">T\u00ednh to\u00e1n c\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a s\u1ed1 ph\u1ee9c l\u00e0 s\u1ed1 l\u01b0\u1ee3ng ph\u1ee9c t\u1ea1p \u0111\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 d\u00e0ng nh\u1ea5t c\u1ee7a c\u00e1c b\u00e0i ki\u1ec3m tra c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia m\u00e0 c\u00e1c \u1ee9ng c\u1eed vi\u00ean n\u00ean ch\u00fa \u00fd.<\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn: \u0110\u1ed1i v\u1edbi b\u00e0i t\u1eadp chuy\u00ean \u0111\u1ec1 s\u1ed1 ph\u1ee9c, c\u00e1c \u1ee9ng c\u1eed vi\u00ean c\u1ea7n s\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a v\u00e0 ho\u1ea1t \u0111\u1ed9ng \u0111\u1ec3 t\u00ednh to\u00e1n c\u00e1c y\u1ebfu t\u1ed1 li\u00ean quan \u0111\u1ec3 t\u00ednh to\u00e1n c\u00e1c y\u1ebfu t\u1ed1 kh\u00e1c nhau c\u1ee7a s\u1ed1 ph\u1ee9c.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">V\u00ed d\u1ee5: Cho hai s\u1ed1 ph\u1ee9c Z1 = 5 &#8211; 7i v\u00e0 Z2 = 2 + 3i. T\u00ecm s\u1ed1 ph\u1ee9c z = Z1 + Z2.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p: <\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Z = Z1 + Z2 = (5 &#8211; 7i) + (2 + 3i) = 7 &#8211; 4i<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_2_Phuong_trinh_tren_tap_hop_phuc\"><\/span>M\u1eabu 2: Ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean t\u1eadp h\u1ee3p ph\u1ee9c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn: S\u1eed d\u1ee5ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh m\u1eabu nh\u01b0 ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t, ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai &#8230;. v\u1edbi c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p \u1ea9n z.<\/p>\n<p dir=\"ltr\">V\u00ed d\u1ee5: <\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/9-chuyen-de-so-phuc.png\" alt=\"\" width=\"650\" height=\"181\"><\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_3_Tim_so_phuc_de_dap_ung_cac_dieu_kien\"><\/span>M\u1eabu 3: T\u00ecm s\u1ed1 ph\u1ee9c \u0111\u1ec3 \u0111\u00e1p \u1ee9ng c\u00e1c \u0111i\u1ec1u ki\u1ec7n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">H\u01b0\u1edbng d\u1eabn: \u0110\u1ec3 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 t\u00ecm c\u00e1c s\u1ed1 ph\u1ee9c \u0111\u1ec3 \u0111\u00e1p \u1ee9ng c\u00e1c \u0111i\u1ec1u ki\u1ec7n \u0111\u00e3 cho, ch\u00fang t\u00f4i l\u00e0m theo c\u00e1c b\u01b0\u1edbc sau:<\/p>\n<ul>\n<li dir=\"ltr\" style=\"line-height: 1.4\">B\u01b0\u1edbc 1: \u0110\u1eb7t Z = A +Ball (A, B thu\u1ed9c v\u1ec1 R)<\/li>\n<li dir=\"ltr\" style=\"line-height: 1.4\">B\u01b0\u1edbc 2: Thay v\u00ec c\u00e1c \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 c\u00f3 \u0111\u01b0\u1ee3c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh hai c\u00e1ch \u1ea9n A v\u00e0 b.<\/li>\n<li dir=\"ltr\" style=\"line-height: 1.4\">B\u01b0\u1edbc 3: Gi\u1ea3i A, b.<\/li>\n<\/ul>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Ch\u00fa \u00fd:<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/10-chuyen-de-so-phuc.png\" alt=\"\" width=\"681\" height=\"171\"><\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">V\u00ed d\u1ee5: <\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\"><img loading=\"lazy\" decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/11-chuyen-de-so-phuc.png\" alt=\"\" width=\"635\" height=\"498\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_4_Bieu_dien_hinh_hoc_cua_cac_so_phuc\"><\/span>M\u1eabu 4: Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc c\u1ee7a c\u00e1c s\u1ed1 ph\u1ee9c <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn: Gi\u1ea3 s\u1eed z = x + yi (x, y thu\u1ed9c v\u1ec1 r). Sau \u0111\u00f3, s\u1ed1 ph\u1ee9c Z \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean m\u1eb7t ph\u1eb3ng ph\u1ee9c theo \u0111i\u1ec3m m (x; y). C\u00e1c \u1ee9ng c\u1eed vi\u00ean c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng d\u1eef li\u1ec7u c\u1ee7a v\u1ea5n \u0111\u1ec1 \u0111\u1ec3 t\u00ecm ra m\u1ed1i quan h\u1ec7 gi\u1eefa X v\u00e0 Y t\u1eeb \u0111\u00f3 suy lu\u1eadn t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m M.<\/p>\n<p dir=\"ltr\"><em>M\u1ed9t s\u1ed1 qu\u1ef9 t\u00edch l\u0169y ph\u1ed5 bi\u1ebfn:<\/em><\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">\u0110\u1ed1i v\u1edbi z = x + yi (x, y l\u00e0 s\u1ed1 th\u1ef1c) th\u00ec:<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 0pt\" role=\"presentation\">X = A: Qu\u1ef9 Zone Z l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = a (song song v\u1edbi OY).<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 0pt\" role=\"presentation\">y = b: v\u00f9ng Z l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng y = b (song song v\u1edbi ox).<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 0pt\" role=\"presentation\">.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 0pt\" role=\"presentation\">.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.7999999999999998;margin-top: 0pt;margin-bottom: 10pt\" role=\"presentation\">.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">V\u00ed d\u1ee5: Cho s\u1ed1 ph\u1ee9c Z = 1 &#8211; 2i. \u0110i\u1ec1u n\u00e0o sau \u0111\u00e2y l\u00e0 bi\u1ec3u di\u1ec5n c\u1ee7a s\u1ed1 ph\u1ee9c w = iz tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9?<\/p>\n<table style=\"border-collapse: collapse;width: 100%;border-color: initial;border-style: none\" border=\"1pt\" cellpadding=\"5pt\">\n<tr style=\"height: 0pt\">\n<td style=\"vertical-align: top;padding: 5pt 5pt 5pt 5pt;overflow: hidden;border: solid #000000 1pt\">\n<p dir=\"ltr\" style=\"line-height: 1.2;margin-top: 0pt;margin-bottom: 0pt\">A. Q (1; 2)<\/p>\n<\/td>\n<td style=\"vertical-align: top;padding: 5pt 5pt 5pt 5pt;overflow: hidden;border: solid #000000 1pt\">\n<p dir=\"ltr\" style=\"line-height: 1.2;margin-top: 0pt;margin-bottom: 0pt\">B. N (2; 1)<\/p>\n<\/td>\n<td style=\"vertical-align: top;padding: 5pt 5pt 5pt 5pt;overflow: hidden;border: solid #000000 1pt\">\n<p dir=\"ltr\" style=\"line-height: 1.2;margin-top: 0pt;margin-bottom: 0pt\">C. M (1; -2)<\/p>\n<\/td>\n<td style=\"vertical-align: top;padding: 5pt 5pt 5pt 5pt;overflow: hidden;border: solid #000000 1pt\">\n<p dir=\"ltr\" style=\"line-height: 1.2;margin-top: 0pt;margin-bottom: 0pt\">D. P (-2; 1)<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 10pt;margin-bottom: 10pt\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Ch\u00fang ta c\u00f3 w = iz = i (1 &#8211; 2i) = 2 + I. \u0111\u01b0\u1ee3c suy ra bi\u1ec3u di\u1ec5n c\u1ee7a s\u1ed1 ph\u1ee9c W l\u00e0 n (2; 1).<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Tr\u1ea3 l\u1eddi: b<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">\n<table style=\"border-collapse: collapse;width: 100.01%;background-color: #fbeeb8\" border=\"1\">\n<tr>\n<td style=\"width: 98.5932%\">\n<p style=\"text-align: center\">\u0110\u1eebng b\u1ecf l\u1ee1 !!<\/p>\n<p style=\"text-align: center\">Ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n h\u1ecdc b\u1eb1ng ti\u1ebfng Anh, gi\u00fap ph\u00e1t tri\u1ec3n t\u01b0 duy theo c\u00e1ch to\u00e0n di\u1ec7n nh\u1ea5t.<\/p>\n<p style=\"text-align: center\">Nh\u1eadn t\u1ed1i \u0111a 40% \u01b0u \u0111\u00e3i ngay t\u1ea1i \u0111\u00e2y!<img decoding=\"async\" style=\"margin-left: auto;margin-right: auto\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/monkeymedia.vcdn.com.vn\/upload\/web\/img\/taimienphiMM.png\" width=\"185\"><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_5_Toi_uu_cua_so_phuc\"><\/span>M\u1eabu 5: T\u1ed1i \u01b0u c\u1ee7a s\u1ed1 ph\u1ee9c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">T\u1ed1i \u01b0u c\u1ee7a s\u1ed1 ph\u1ee9c l\u00e0 m\u1ed9t h\u00ecnh th\u1ee9c c\u1ee7a m\u1ed9t v\u1ea5n \u0111\u1ec1 ph\u1ee9c t\u1ea1p \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng cao m\u00e0 c\u00e1c \u1ee9ng c\u1eed vi\u00ean c\u1ea7n ph\u1ea3i ch\u00fa \u00fd \u0111\u1eb7c bi\u1ec7t n\u1ebfu h\u1ecd mu\u1ed1n \u0111\u1ea1t \u0111\u01b0\u1ee3c s\u1ed1 \u0111i\u1ec3m t\u1eeb 8 tr\u1edf l\u00ean.<\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn: S\u1eed d\u1ee5ng ki\u1ebfn \u200b\u200bth\u1ee9c c\u01a1 b\u1ea3n nh\u01b0: Li\u00ean h\u1ec7 b\u1ea5t b\u00ecnh \u0111\u1eb3ng gi\u1eefa trung b\u00ecnh v\u00e0 trung b\u00ecnh, bunhia-trunk-atorquity, b\u1ea5t b\u00ecnh \u0111\u1eb3ng h\u00ecnh h\u1ecdc v\u00e0 m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 c\u00f4ng c\u1ee5 sau \u0111\u00e2y:<\/p>\n<p dir=\"ltr\">B\u00e0i to\u00e1n c\u00f4ng c\u1ee5 1:<\/p>\n<p dir=\"ltr\">Cho m\u1ed9t v\u00f2ng tr\u00f2n c\u1ed1 \u0111\u1ecbnh <\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/p>\n<p dir=\"ltr\">Th1: A thu\u1ed9c v\u1ec1 v\u00f2ng tr\u00f2n (T) <\/p>\n<p dir=\"ltr\">Ch\u00fang t\u00f4i c\u00f3: <\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">AM \u0111\u1ea1t gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u l\u00e0 0 khi m tr\u00f9ng v\u1edbi<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">AM \u0111\u1ea1t gi\u00e1 tr\u1ecb t\u1ed1i \u0111a b\u1eb1ng 2R khi M l\u00e0 \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng v\u1edbi A qua i<\/p>\n<\/li>\n<\/ul>\n<p dir=\"ltr\">TH2: A kh\u00f4ng thu\u1ed9c v\u1ec1 v\u00f2ng tr\u00f2n <\/p>\n<p dir=\"ltr\">\u0110\u1eb7t b, c l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng qua a, i v\u00e0 v\u00f2ng tr\u00f2n <\/p>\n<p dir=\"ltr\">Gi\u1ea3 s\u1eed ab<\/p>\n<p dir=\"ltr\">+ N\u1ebfu A n\u1eb1m ngo\u00e0i v\u00f2ng tr\u00f2n <\/p>\n<p dir=\"ltr\">Am&gt; = ai &#8211; im = ai &#8211; ib = ab, ph\u01b0\u01a1ng tr\u00ecnh x\u1ea3y ra khi m tr\u00f9ng kh\u1edbp B.<\/p>\n<p dir=\"ltr\">Am =<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/12-chuyen-de-so-phuc.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\">+ N\u1ebfu A n\u1eb1m trong v\u00f2ng tr\u00f2n <\/p>\n<p dir=\"ltr\">AM&gt; = II &#8211; IA = IB &#8211; IA = AB, Ph\u01b0\u01a1ng tr\u00ecnh x\u1ea3y ra khi m tr\u00f9ng kh\u1edbp B.<\/p>\n<p dir=\"ltr\">Am =<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/13-chuyen-de-so-phuc.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\">V\u00ec v\u1eady, khi M tr\u00f9ng v\u1edbi B, AM \u0111\u1ea1t \u0111\u1ebfn gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u v\u00e0 khi M tr\u00f9ng v\u1edbi C, AM \u0111\u1ea1t \u0111\u1ebfn gi\u00e1 tr\u1ecb t\u1ed1i \u0111a.<\/p>\n<p dir=\"ltr\">Xem th\u00eam: C\u1ea5u tr\u00fac b\u00e0i ki\u1ec3m tra to\u00e1n c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia 2024 &amp; gi\u1ea3i ph\u00e1p hi\u1ec7u qu\u1ea3<\/p>\n<p dir=\"ltr\">B\u00e0i to\u00e1n c\u00f4ng c\u1ee5 2:<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Cho hai v\u00f2ng tr\u00f2n (T1) v\u1edbi trung t\u00e2m I, RADIUS R1; V\u00f2ng tr\u00f2n (T2) c\u00f3 trung t\u00e2m J, b\u00e1n k\u00ednh R2. T\u00ecm v\u1ecb tr\u00ed c\u1ee7a \u0111i\u1ec3m M \u1edf tr\u00ean (T1), \u0111i\u1ec3m N \u1edf tr\u00ean (T2) \u0111\u1ec3 Mn \u0111\u1ea1t \u0111\u1ebfn gi\u00e1 tr\u1ecb t\u1ed1i \u0111a v\u00e0 t\u1ed1i thi\u1ec3u.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">\u0110\u1eb7t d l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua i, j; d C\u1eaft v\u00f2ng tr\u00f2n (T1) t\u1ea1i hai \u0111i\u1ec3m ri\u00eang bi\u1ec7t A, B (gi\u1ea3 s\u1eed JA&gt; JB); D Cut (T2) t\u1ea1i hai \u0111i\u1ec3m ri\u00eang bi\u1ec7t C, D (gi\u1ea3 s\u1eed ID&gt; IC).<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">V\u1edbi b\u1ea5t k\u1ef3 \u0111i\u1ec3m m \u1edf tr\u00ean (T1) v\u00e0 b\u1ea5t k\u1ef3 \u0111i\u1ec3m N n\u00e0o \u1edf tr\u00ean (T2).<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Ch\u00fang t\u00f4i c\u00f3: <\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Mn =<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Mn&gt; = | T\u00f4i &#8211; trong | &gt; = | Ij &#8211; im &#8211; jn | = | IJ &#8211; R1 + R2 | = BC, ph\u01b0\u01a1ng tr\u00ecnh x\u1ea3y ra khi M tr\u00f9ng v\u1edbi B v\u00e0 N tr\u00f9ng v\u1edbi C.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/14-chuyen-de-so-phuc.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">V\u00ec v\u1eady, khi M tr\u00f9ng v\u1edbi A v\u00e0 N tr\u00f9ng v\u1edbi D, Mn \u0111\u1ea1t \u0111\u1ebfn gi\u00e1 tr\u1ecb t\u1ed1i \u0111a v\u00e0 khi M tr\u00f9ng v\u1edbi B v\u00e0 N tr\u00f9ng v\u1edbi C, Mn \u0111\u1ea1t \u0111\u1ebfn gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">B\u00e0i to\u00e1n 3: <\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Cho hai v\u00f2ng tr\u00f2n <\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i ph\u00e1p:<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">\u0110\u1eb7t h l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a i tr\u00ean d.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">\u0110o\u1ea1n IH c\u1eaft v\u00f2ng tr\u00f2n (T) t\u1ea1i J.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">V\u1edbi m thu\u1ed9c v\u1ec1 d\u00f2ng [denta]N thu\u1ed9c v\u1ec1 v\u00f2ng tr\u00f2n <\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">Mn&gt; = in &#8211; im&gt; = ih &#8211; ij = jh = const, ph\u01b0\u01a1ng tr\u00ecnh x\u1ea3y ra khi m tr\u00f9ng H v\u00e0 n tr\u00f9ng kh\u1edbp I.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/15-chuyen-de-so-phuc.png\" alt=\"\" width=\"100%\"><\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">V\u00ec v\u1eady, khi m tr\u00f9ng v\u1edbi H; N tr\u00f9ng v\u1edbi J, sau \u0111\u00f3 Mn \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t.<\/p>\n<p dir=\"ltr\" style=\"line-height: 1.4\">\n<p dir=\"ltr\" style=\"line-height: 1.4;margin-top: 0pt;margin-bottom: 10pt\">V\u1edbi ki\u1ebfn \u200b\u200bth\u1ee9c v\u00e0 k\u1ef9 n\u0103ng c\u1ee7a c\u00e1c con s\u1ed1 ph\u1ee9c t\u1ea1p \u0111\u01b0\u1ee3c trang b\u1ecb t\u1eeb b\u00e0i vi\u1ebft n\u00e0y c\u1ee7a Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef, b\u1ea1n ho\u00e0n to\u00e0n c\u00f3 th\u1ec3 t\u1ef1 tin chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao trong k\u1ef3 thi to\u00e1n h\u1ecdc tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia. Xem x\u00e9t th\u01b0\u1eddng xuy\u00ean, th\u1ef1c h\u00e0nh c\u00e1c gi\u1ea3i ph\u00e1p li\u00ean t\u1ee5c v\u00e0 kh\u00f4ng qu\u00ean tham kh\u1ea3o c\u00e1c t\u00e0i li\u1ec7u xem x\u00e9t thi kh\u00e1c \u0111\u1ec3 c\u1ee7ng c\u1ed1 ki\u1ebfn \u200b\u200bth\u1ee9c to\u00e0n di\u1ec7n. Ch\u00fac b\u1ea1n h\u1ecdc h\u1ecfi hi\u1ec7u qu\u1ea3 v\u00e0 \u0111\u1ea1t \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 t\u1ed1t nh\u1ea5t trong k\u1ef3 thi!<\/p>\n<p>Ngu\u1ed3n: <a href=\"https:\/\/www.ckconitsha.com\/vn\/\">https:\/\/www.ckconitsha.com\/vn\/<\/a> T\u00e1c gi\u1ea3: <a href=\"https:\/\/www.ckconitsha.com\/vn\/author\/nguyenlandung\">Nguy\u1ec5n L\u00e2n d\u0169ng<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ea1n \u0111ang \u0111\u1ea5u tranh \u0111\u1ec3 xem x\u00e9t k\u1ef3 thi to\u00e1n c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc qu\u1ed1c gia, \u0111\u1eb7c bi\u1ec7t l\u00e0 ch\u1ee7 \u0111\u1ec1 s\u1ed1 ph\u1ee9c. \u0110\u1eebng lo l\u1eafng! T\u00f3m t\u1eaft ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 c\u00e1c s\u1ed1 ph\u1ee9c t\u1ea1p (l\u00fd thuy\u1ebft v\u00e0 b\u00e0i t\u1eadp) m\u00e0 kh\u1ec9 cung c\u1ea5p trong b\u00e0i vi\u1ebft n\u00e0y s\u1ebd l\u00e0 ng\u01b0\u1eddi b\u1ea1n \u0111\u1ed3ng h\u00e0nh m\u1ea1nh&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[100],"tags":[],"class_list":["post-13498","post","type-post","status-publish","format-standard","hentry","category-kien-thuc"],"_links":{"self":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/13498","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/comments?post=13498"}],"version-history":[{"count":2,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/13498\/revisions"}],"predecessor-version":[{"id":16007,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/13498\/revisions\/16007"}],"wp:attachment":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/media?parent=13498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/categories?post=13498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/tags?post=13498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}