解题方法
1 . 设
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5083da35f1c479de1ce005364043da3.png)
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b958dc0b71559463006d1d5894d12c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5083da35f1c479de1ce005364043da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e3fdecd7a072eac3619a2b5082e63a.png)
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解题方法
2 . 借助复数、三角及向量的知识,可以研究平面上点及图像的旋转问题.请尝试解答下列问题:
(1)在直角坐标系中,已知点
的坐标为
,将
绕坐标原点O逆时针方向旋转
至
.求点
的坐标;
(2)设向量
,把向量
按顺时针方向旋转
角得到向量
,求向量
对应的复数;
(3)设
为不重合的两个定点,将点
绕点
按逆时针旋转
角得到点
,判断点
是否能够落在直线
上,若能,试用
表示相应
的值,若不能,说明理由.
(1)在直角坐标系中,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc69e8d3fd54bb07d183a5ce38234e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/873c064546108a5bce78bb71bc1e4a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870707dd29b0411bd3c348d662529df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e7adca5c1f19c6fc21664a2a928ee9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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3 . 已知
为虚数,若
,且
.
(1)求
的实部的取值范围;
(2)设
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a7d9facada7486cefdbc8898809e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9bda5d47fd148f8a0c16dc0a55dd6e0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7174364de68e1553ad217179203cd6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee13964464e17696a9331539dacef680.png)
您最近一年使用:0次
2022-06-28更新
|
1648次组卷
|
15卷引用:上海市上海师范大学附属中学闵行分校2021-2022学年高一下学期期末数学试题
上海市上海师范大学附属中学闵行分校2021-2022学年高一下学期期末数学试题(已下线)专题14 复数(练习)-2福建师范大学附属中学2022-2023年高一下学期期中考试数学试题第12章《复数》单元达标高分突破必刷卷(培优版)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(苏教版2019必修第二册)高一复数重难点提高卷-【同步题型讲义】(已下线)模块二 专题3 《复数》单元检测篇 B提升卷 (北师大版)(已下线)模块二 专题2 《复数》单元检测篇 B提升卷(已下线)模块二 专题4 复数 单元检测篇 B基础卷(人教B)(已下线)模块二《复数》单元检测篇 B基础卷 (北师大版)(已下线)模块二 专题4 《复数》单元检测篇 B提升卷 (苏教版)(已下线)核心考点02复数(2)(已下线)专题7.8 复数全章综合测试卷(提高篇)-举一反三系列(已下线)复数的概念与运算(已下线)7.2.2复数的乘、除运算——课后作业(提升版)(已下线)7.2.2复数的乘、除运算——课后作业(巩固版)
4 . 设复平面中向量
对应的复数为
,给定某个非零实数
,称向量
为
的
向量.
(1)已知
,
,求
;
(2)对于复平面中不共线的三点
,
,
,设
,
,
,求
;
(3)设
,
,
的
向量分别为
,
,
,已知
,
,
,求
的坐标(结果用
,
,
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1dbb4c7999d45d14b499e433a09137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f1e00c3019c29a5fc7a16e3d3b3e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8626ed40ac561244d7a7d78fdb24bc.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774e4c61b6568d292d5bc576d3310d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47d5a819f2e82edbac8a82b05f64501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e1c7761a2fbb1478d7aa767aaf792a.png)
(2)对于复平面中不共线的三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14958b2ff6f32f726a32cd19edd6580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce82b5f1ceed0d68799e2b7e6b7b1fd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1b55b0740a656f575c1c840e86b3be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215810926adc373683112851fd0ce865.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e81a4a797612364e40633d513025f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b87d9af9b910dab963d0958e514f8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8b2329d17c216854810353e8986c4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350febbbd2a60e7f7d52d3a913983f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b52fad476f828f36de6eb8910497329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08493c1e001d85731cb4863ec38857fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992de06f8effea20895e0ea2262010b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5d1fe2ed4027eaec2abdc0ada9db47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931d593e16a7e6e82b5c2418e7afe6db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720da193aaf7aa394aa2778d32b7737e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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5 . 设复数
是关于
的方程
(
且
,
为实数)的虚数根.
(1)若
,求
的取值范围以及
的值;
(2)若
,求所有虚数
的实部之和
(用仅含有字母
的式子表示);
(3)设虚数
对应的位置向量为
,记
,若
,求
的取值范围(用仅含有字母
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0015e474667c4588fda8d0cc5774b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429671166ab81044097fc277f179ee96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设虚数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83fb869e015cc9558c2ac40406db151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf7adcc976209d4b686156120bea276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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