From 53abe89535d32c4fd48ee6703e193e9605dfb73e Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 11:46:07 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A32=E6=96=B0=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 218 ++++++++++++++++++++++++++++++- 2 files changed, 218 insertions(+), 3 deletions(-) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 25c18668..438adcf7 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -94,3 +94,6 @@ 20240125-114309 023865:023872 +20240125-114602 +023873:023882 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 2e9e830a..9da37e1b 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -65742,7 +65742,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023882" + ], "remark": "", "space": "", "unrelated": [] @@ -391556,7 +391558,9 @@ "20230128\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023879" + ], "remark": "", "space": "4em", "unrelated": [] @@ -644016,6 +644020,212 @@ "space": "4em", "unrelated": [] }, + "023873": { + "id": "023873", + "content": "若复数 $z$ 满足 $(1+\\mathrm{i}) z=2$, 则复数 $z$ 的虚部为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023874": { + "id": "023874", + "content": "若复数 $z=\\dfrac{2 \\mathrm{i}}{1+\\mathrm{i}}$, 则 $z$ 的共轭复数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "040799" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023875": { + "id": "023875", + "content": "若 $x \\in \\mathbf{R}$, 则``$x=2$''是``复数 $z=(x^2-4)+(x+2) \\mathrm{i}$ 为纯虚数''的\\blank{50}条件.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023876": { + "id": "023876", + "content": "若 $(1+\\mathrm{i}) \\cdot z=\\sqrt{3}\\mathrm{i}$, 则复数 $z$ 在复平面内对应的点位于第象限.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023877": { + "id": "023877", + "content": "已知 $z=1-\\mathrm{i}$, 计算 $\\dfrac{1+3 i}{\\overline{z}}+\\sqrt{2}|z| \\mathrm{i}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023878": { + "id": "023878", + "content": "若复数 $z$ 满足 $z-2 \\mathrm{i}=\\dfrac{1}{1-\\mathrm{i}}$, 则复数 $z$ 在复平面内的点到原点的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023879": { + "id": "023879", + "content": "若复数 $z_1=1+2 a \\mathrm{i}$, $z_2=a-\\mathrm{i}$($a \\in \\mathbf{R}$), 集合 $A=\\{z|| z-z_1 | \\leq \\sqrt{2}\\}$, $B=\\{z|| z-z_2 | \\leq 2 \\sqrt{2}\\}$, 且 $A \\cap B=\\varnothing$, 则实数 $a$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "014057" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023880": { + "id": "023880", + "content": "若 $z=x+y \\mathrm{i}$($x, y \\in \\mathbf{R}$), 且满足 $|z+2|=-x$, 则复数 $z$ 对应点的轨迹是 \\bracket{20}.\n\\fourch{圆}{抛物线}{椭圆}{双曲线}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023881": { + "id": "023881", + "content": "已知复数 $z$ 满足 $z \\cdot \\overline{z}+(1-2 \\mathrm{i}) z+(1+2 \\mathrm{i}) \\overline{z}=3$, 求 $|z|$ 的最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023882": { + "id": "023882", + "content": "已知平行四边形的三个顶点分别对应复数 $2 \\mathrm{i}, 4-4 \\mathrm{i}, 2+6 \\mathrm{i}$, 求第四个顶点对应的复数.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "002010" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0