名校
1 . 下列命题为真命题的是( )
A.复数![]() |
B.若![]() ![]() ![]() |
C.若复数![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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解题方法
2 . (1)计算
;
(2)已知
,
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df29d2ddd1a04ece8a1e2647814a0b2.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e50a91f469e77f35636f982e75f50a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437601a277901f79aa3d6a4b955cf72d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c98466484e09a9a4ff6b10785d6715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17cc100e36303b3566d91e4756594cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8275b23b7e128bfdd61c76f4af8954.png)
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解题方法
3 . 已知
,且
,
为虚数单位,则
的最大值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707aed47159fae11f47e464c548a0b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a12dde0b5b3855c307fefe7a0e9c0cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579743813856e2a9183f5ec6eaaefbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4b22a3e669a5ad4a11888e0b878a1c.png)
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4 . 已知复数
,其中
是实数.
(1)若
,求
的值;
(2)若
是实数,求
的值;
(3)若复数
在复平面内对应的点在第二象限,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac002b4ffc7258a6e578b2ec51543dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c9a9e100b6afb2943edb9109ecfe96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157ec5b131fd2d3d0d2f49c6cb4d5aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 已知复数
,
,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
A.若![]() ![]() |
B.若![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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解题方法
6 . 已知复数
,
,其中i为虚数单位.
(1)若
,求
;
(2)若复数z为纯虚数,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aabd07b75e7a9579c1ca8abbbabaeba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
(2)若复数z为纯虚数,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
7 . 复数
在复平面内对应的点为
,原点为
,i为虚数单位,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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解题方法
8 . 下列四个命题正确的是( )
A.若![]() ![]() |
B.如图所示,在平面四边形![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.设向量![]() ![]() ![]() |
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9 . (1)已知
,若
为实数,求
的值.
(2)已知复数
满足
,若复数
是实系数一元二次方程
的一个根,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c24ecf9e59082e563372b12981d03fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5271d8258796a0cbf1ddcfc541573e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)已知复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e9585a1da28d403536ea48b4c37a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6fbaf8ca78b7c29705e3fcd784783d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b800b7d6a688abf8a3018c133cec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
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10 . 已知非零复数
,其共轭复数分别为
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4da30f4906d97d276b3e1f2ac8aed8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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