1 . 分式线性变换又称为莫比乌斯变换,它是定义在复数集中形如
的变换,其中w称为z的“像”,z称为w的“原像”.
(1)若
,求i的“像”以及
“原像”;
(2)若
,
,求证:
的充要条件是
;
(3)若
,
,z满足
,求z的“像”在复平面上所构成图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7192583ba609cb106ade4e4488dd15.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49800f57be0280b700ec3e43a5c81449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186bb9626ba707655b540871c863bdc4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c2c9d5ac204f207fc4edfd2160e7b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa828aaf76504bf5e4a749e28ff3815f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f525f4df6befc8fcf566d6f4f7d2150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475e17c54117d4b846275df1ba74b26a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adebd26bdc1c9f97d05f111fb22b1073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b83b93d6b7241c2db386d5571b9932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88fe440162463512c88bb099ea959ff.png)
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2022-04-25更新
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2卷引用:上海交通大学附属中学2021-2022学年高一下学期期中数学试题