1 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5d2ccba293fac59443cf6f0cd3c408.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5d2ccba293fac59443cf6f0cd3c408.png)
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解题方法
2 .
被称为欧拉公式.我们运用欧拉公式,可以推导出倍角公式.如:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4511b4a678755f69f4a9a82b117cca3c.png)
.类比方法,我们可以得到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c87e34f4681791e0a5d00fd70576030.png)
____ (用含有
的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc0ab4d45a4bef21ba8ae793f2e76f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4511b4a678755f69f4a9a82b117cca3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ef5b2ea33b6ea08df130ce079aac19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c87e34f4681791e0a5d00fd70576030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48345d239aaf8e9ca1ff2846c08a99.png)
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解题方法
3 . 已知
(
为虚数单位).设集合
,则集合
中的元素在复平面上对应点所形成图形的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3a7e1ea06b2eb0061ad24605eb7fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02822aa4caeab52a3b2e8d9dba18d74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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4 . 复数的乘方:实数集
中正整数指数的运算律,在复数集
中仍然成立,只不过是要把运算的结果写成复数的代数形式罢了.即若
,m,n是正整数,则
①
; ②
;③
;④
.
复数的除法运算法则:复数的除法,实质上就是分母“实数化”——将分母化为实数,即分子、分母同乘以分母的共轭复数.类似于以前所学的分母“有理化”.于是,我们得到,当
,且
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ce4f6edb26ddfc86b73b0c9443c37e.png)
______________ .
的乘方的性质及其应用:在计算
的高次幂的值时,常常利用
,
简化运算.如计算
时,先将其表示成
与
的积,再将
看成是
,于是得到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f086009af2e86309dd8688f1f97c27.png)
___________ .
设
,利用复数的四则运算法则,可以得到
具有下面的性质:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fdfb84247dffc8fcc6678d34e00dd2.png)
_________ ; ②
; ③
; ④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c3c68fb14a6c63bf4d0869c71e6513.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f015ed8e497b4394053ddd19683a98f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe639d6800b34618d379dd1fc07d74af.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336ad2461f5bc92f6f4e6f7d981983c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3d8634bc85df0a4a04550cca29231c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f193a2071132d8466a161cefcc50c4a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a129424a8b6a52dfd0c6568a266669f.png)
复数的除法运算法则:复数的除法,实质上就是分母“实数化”——将分母化为实数,即分子、分母同乘以分母的共轭复数.类似于以前所学的分母“有理化”.于是,我们得到,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b40d453ac56a449af2c33e31ff49c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bff71e0a1fb212d900f59491248bf3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ce4f6edb26ddfc86b73b0c9443c37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf922fbceea012b857449a80079adc8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abea11dc55beb34183e5542443c98c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c7d11e443ee9aeca7e45e6d31afe1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064b0e7b2494d7341339be6a80961158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7ad7ce320f21c4b1f60bc8e381239b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5faa2af08cf50fa3efada313a694d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c167774cf4c5c67c0af0a5b1cb5a6528.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5faa2af08cf50fa3efada313a694d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048c2a7371541a685e4d66b38b5c282c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f086009af2e86309dd8688f1f97c27.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afc2753abf67f40c8070fda7538cda6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fdfb84247dffc8fcc6678d34e00dd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0377e5c91846b3a0e71f4cc03ca1c9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080397a23c2bc5b9d87261e3795d5d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c3c68fb14a6c63bf4d0869c71e6513.png)
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5 . 写出一个复数z,使得z满足
且
,则z可以为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebb6b7b4cbc9c62bbf990d693efeee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f05368c016ed03b4c6bb3060c28add.png)
您最近一年使用:0次
2022-04-19更新
|
321次组卷
|
2卷引用:福建省龙岩市一级校联盟(九校)2021-2022学年高一下学期半期考(期中)数学试题
6 . 已知下列命题:
(1)复数
不是实数;(2)当
时,
;(3)若复数
,当且仅当
时,
为虚数;(4)若
时,有
,则
且
.其中真命题的个数是_______ .
(1)复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eed3d568acf369a315c7ab41c081049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707aed47159fae11f47e464c548a0b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6ca7eb28f429391d546d31387f5241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554a7f956562e8ea70faf6b7780e1138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4063994562bb3788c4999b82ff82b3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759b29a7b2b3735306f1a650355a7858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc330a9671536bc46fa244b4ceebcf9.png)
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名校
7 . 已知虚数
是1的一个四次方根,复数
,
,用列举法表示满足条件的
组成的集合为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0214abb30bbf692ba667fbdca05504e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
您最近一年使用:0次
2021-07-20更新
|
184次组卷
|
2卷引用:上海市延安中学2020-2021学年高一下学期期末数学试题