1 . 复数
,则以下正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd85688279a50d3d6e7091d88e70a2af.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知,求
的值.
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3 . 已知,求
.
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4 . 已知的虚部可能为( )
A.![]() | B.![]() | C.1 | D.0 |
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解题方法
5 . 已知复数的三角形式为
.
(1)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb0e25bbccbee4a1b9db38b49e87978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb0e25bbccbee4a1b9db38b49e87978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30deb1f343048675b9b231620369668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795806b48c253f51784994dedf0d8502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8536fdc54e3e4fe48b4dd8d75a52ee89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
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6 . 设
、
是无穷复数数列,满足对任意正整数n,关于x的方程
的两个复根恰为
、
(当两根相等时
).若数列
恒为常数,证明:
(1)
;
(2)数列
恒为常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80289c798034033f2f7cfcd7590f2344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52cabfa2464501decf05aed007cbaf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841f4ea50fa0c2b4c6e47dc04597abba.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561d594ed04e6652c75dac56259f4292.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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7 . 设
,且
.
(1)已知
,求
的值;
(2)若
,设集合
,
,求复平面内
对应的点集表示的曲线的对称轴;
(3)若
,
,是否存在
,使得数列
、
、
满足
(
为常数,且
)对一切正整数
均成立?若存在,试求出所有的
,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255483db09b1e523a4fcc1f618b98ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30fb46705507031e9a14ed4ebc643be.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb634a77583d09f48eab80c5635e2675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ff004d412c298ad84ca986f44d2d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a03e218e8fd89aea272737dcdf18d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27672b93ffc842f8a2555b5754cb0cf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51489fd22b18fff8c79ea7c02f2e4c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5759643249b011f1094e38c2f3166bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5094476a315a9f205ac03829ade1419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24431f390ba671b4de0d6abaeb9cf476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
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8 . 已知复数
满足
,(其中
是虚数单位),则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8e1d07ecc02f4d25e7197036bb42b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50f4898fc5f344dffa87325c1fa30a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a40e2b6c49f849119ad4a3f2e79530.png)
A.2 | B.6 | C.![]() | D.![]() |
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2020-01-31更新
|
3432次组卷
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5卷引用:2017届上海市七宝中学高三下学期综合测试五(5月)数学试题