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收录高三寒假作业32新题

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wangweiye7840 2024-01-25 11:46:07 +08:00
parent 1026d5f2ff
commit 53abe89535
2 changed files with 218 additions and 3 deletions
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3
工具v2/文本文件/新题收录列表.txt
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@ -94,3 +94,6 @@
20240125-114309
023865:023872
20240125-114602
023873:023882

218
题库0.3/Problems.json
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@ -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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
@ -720005,7 +720215,9 @@
"20230601\t王伟叶"
],
"same": [],
"related": [],
"related": [
"023874"
],
"remark": "",
"space": "",
"unrelated": []