名校
1 . 设
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8b0a630e156f5ef0ef8bd3ebfee6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e4e1addca1918db8ce767ad18e3c3e.png)
A.充分不必要条件 | B.必要不充分条件 | C.充要条件 | D.既不充分也不必要条件 |
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2023-03-13更新
|
1396次组卷
|
7卷引用:江苏省常州市前黄高级中学2023-2024学年高三上学期期初考试数学试题
名校
解题方法
2 . “虚数”这个名词是17世纪著名数学家、哲学家笛卡尔
创制的,直到19世纪虚数才真正闻人数的领域,虚数不能像实数一样比较大小.已知复数
,
且
(其中i是虚数单位
,则复数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f86e73ffea7be74070603915298e0a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70c2519610d6d1d6d0855b0f27dfc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1354c0e46fb42bf7cc8a2152d5bfd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知虚数
满足
,
为虚数单位.
(1)若
是纯虚数,求
;
(2)求证:
为纯虚数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839ba7c0f1fc30151d18a2e337951dd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f89433ce4c5a6129757759c3d99518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5960b7f7052b0676f9b2f0b3f0014b.png)
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