1 . 已知
,则
的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9479c475b01323e739ccdc4b54cb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
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2021-07-22更新
|
515次组卷
|
2卷引用:全国高中数学联赛模拟试题(二)
2 . 已知复数
(i虚数单位),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459417258bb1ac3d18fc5d26931dc00c.png)
______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa24d167be1a32edf57b63f6dba3797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459417258bb1ac3d18fc5d26931dc00c.png)
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3 . 已知复数a、b、c满足
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3d34168f1ebbe52794e4d20a0dcf8d.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12599cb36f2c567725589693b1a69fbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3d34168f1ebbe52794e4d20a0dcf8d.png)
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4 . 求证:存在非零复数c与实数d,使得对于一切模长为1的复数
均有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3185a496b769c519c56b007527aaf62b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cec18bd06c3d0d1a5a1be8b4627b5c7.png)
您最近一年使用:0次
5 . 设点Z是单位圆
上的动点,复数W是复数Z的函数:
,试求点W的轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f21d56171685d8ebbb90062f3f965c2.png)
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6 . 已知
,存在唯一的
,使得
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707aed47159fae11f47e464c548a0b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5215ead9dda7b1eb968ae4e41b28b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d037a6f4bfe8fd31cf0107b7011970e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4fbc796def901bda4cb9e6083f8359.png)
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7 . 已知实数
.若方程
的三个复数根在复平面上构成边长为
的正三角形,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e2c1d0c2c5336321d68a4cbc689e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fd47cc79cbc128dd346e67d529aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24d95e0548b340af8783a57bdfd05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
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8 . 若复数
满足条件
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39784a6667e741635d5004144020f12.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308f43c468d83daffea9db100e24c41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/415df6ff409e0483ea85f64957d5d8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39784a6667e741635d5004144020f12.png)
您最近一年使用:0次
9 . 若复数
满足
,则
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/197f7ebfe43eed5f13afe52b46642768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41087ab4ce636246d2f9ab4ed430edfa.png)
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10 . 设方程
的所有复数
、
.则
等于( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f628d2b2e2d656aae533c9373b4445a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1898d6fb68464c6dddd3018fb8c2b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2005ec1fab176d3ada2b01c56db1de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e2b6ee58b0979c226776486f3995c4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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