2024高三上·全国·专题练习
1 . 设
是虚数,
(1)求证
为实数的充要条件为
;
(2)若
,推测
为实数的充要条件;
(3)由上结论,求满足条件
,及实部与虚部均为整数的复数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ae50806d8c14f0275864b30e9f30a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6db0e748196e89b9d821e0289c751d9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2d495bb0ee1fda8edb853595e3e472.png)
(3)由上结论,求满足条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ae288e6e67e9248046d57e6a779763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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解题方法
2 . 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1196db72f1d2df1ded968a6762c37bab.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ac39b25d00b9a520c40f7087e42737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1196db72f1d2df1ded968a6762c37bab.png)
您最近一年使用:0次