1 . 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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解题方法
2 . 若复数
满足
(
为虚数单位),则
的虚部为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49ccb0dd333d698d579ef7724c79b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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2022-06-23更新
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3卷引用:安徽省芜湖市顶峰艺术高级中学2021-2022学年高一下学期期末数学试题
安徽省芜湖市顶峰艺术高级中学2021-2022学年高一下学期期末数学试题辽宁省渤海大学附属高级中学2021-2022学年高一下学期第二次阶段性考试数学试题(已下线)第12章:复数 章末检测试卷-【题型分类归纳】2022-2023学年高一数学同步讲与练(苏教版2019必修第二册)
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3 . 复数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e1007fbbcd554c7dc4980f9eab50dd.png)
_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e1007fbbcd554c7dc4980f9eab50dd.png)
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4 . 若复数
(
为虚数单位),则
的模
=___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43b3db5e9a31700957aa6f83c31d130.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/c042c0c7e253a65f770583c5c6696770.png)
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2020-12-25更新
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3卷引用:安徽省六安市田家炳实验中学2022-2023学年高一下学期期末考试数学试题
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5 . 已知复数
满足
(
为虚数单位),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a176cfc17acf73eba234dfccadd8f1e.png)
____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0288efd9e34584bcb2fa5e31fd4d4783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a176cfc17acf73eba234dfccadd8f1e.png)
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2020-12-23更新
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2卷引用:安徽省亳州市涡阳第—中学2020-2021学年高一下学期期末数学试题
6 . 已知复数
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7791d7e001d437913e9e829c63879a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
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7 . 凸多边形中,四边形有2条对角线,五边形有5条对角线,则凸十二边形的对角线条数为______ .
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8 . 已知复数
,
的共轭复数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca6c17df8a51bb6492426fddcfb622.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a2469d262b410986d365b9c6a617d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca6c17df8a51bb6492426fddcfb622.png)
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2020-08-03更新
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6卷引用:安徽省黄山市2020-2021学年高一下学期期末数学试题
9 . 已知变量
,由它们的样本数据计算得到
的观测值
,
的部分临界值表如下:
![](https://img.xkw.com/dksih/QBM/2020/7/21/2510521014026240/2513668803207169/STEM/08eea708-039f-4ee7-96ca-6808a345fbdb.png)
则最大有________ 的把握说变量
有关系.(填百分数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0010cb466163db1349fc1040f6b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2581192317ef233ccdccfc48ac29b52b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2e561407ac581068c6313a510c4e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2581192317ef233ccdccfc48ac29b52b.png)
![](https://img.xkw.com/dksih/QBM/2020/7/21/2510521014026240/2513668803207169/STEM/08eea708-039f-4ee7-96ca-6808a345fbdb.png)
则最大有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0010cb466163db1349fc1040f6b439.png)
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10 . 若复数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882bff376e1d71865bd23b747ef78a66.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad770a814244c640a664d6f35a136e06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882bff376e1d71865bd23b747ef78a66.png)
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2019-07-29更新
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2卷引用:安徽省滁州市九校联谊会(滁州二中、定远二中等11校)2018-2019学年高二下学期期末数学(文)试题