1 . 已知
为虚数单位,复数
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a176cfc17acf73eba234dfccadd8f1e.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1831edb185cd71e0a092a5e1e0c91bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a176cfc17acf73eba234dfccadd8f1e.png)
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2 . 欧拉公式
(i为虚数单位,
)是由瑞士著名数学家欧拉发现的,它将指数函数的定义域扩大到复数,建立了三角函数和指数函数之间的关系,它被誉为“数学中的天桥”.根据此公式可知,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f6c5f351af3d5275cfc45f947a9bef.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077d3127494e1bde3bfe6ab71e9974b5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfa007ea5744567c67bebd638bd5cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f6c5f351af3d5275cfc45f947a9bef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077d3127494e1bde3bfe6ab71e9974b5.png)
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