名校
解题方法
1 . 求值计算:
(1)
,求
的值
(2)
,求
的值
(3)复数z满足
(
为虚数单位),求z
(4)复数z满足:
,且z在复平面内对应的点位于第三象限,求
的值.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d3b6c316c70ed7a88f9aed6454d5ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba20c2fe92bf98bf49b4e44b80919b4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4720fa72e415b389f82a794026559ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680c514271ab4a9c8424873bd5e2b154.png)
(3)复数z满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5661b4d48239c090583080987cfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
(4)复数z满足:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207e80766a7e6837927a0f04b0612b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e26e4e9b179160da5ce576e8fbd74e.png)
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名校
2 . 已知复数
、
对应的向量为
.
(1)若向量
,且
,
.求
对应的复数
;
(2)容易证明:
,类比到对应的向量,请写出类似的结论,并加以证明;
(3)设
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5cdedb6f4384fda29fb4508ba6fcc5.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c931438cd1de4180c622d66aee1de431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbf8cf890e1bab18f37152ef5da7dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c97d2a35ee85fa0b51eeaeb1ce1f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4302196fdb56536ddc2f2a3c2e9073e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
(2)容易证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8c8b8610bef469c87bb73919310477.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e294bd40af7a49ac1fadca723499c229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
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3卷引用:上海市曹杨第二中学2020-2021学年高一下学期5月月考数学试题
上海市曹杨第二中学2020-2021学年高一下学期5月月考数学试题(已下线)专题7.7 复数的运算大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)高一复数重难点提高卷-【同步题型讲义】
3 . 已知
R,复数
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526c6e33166cdaadce9d0226b67642c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362a7f65ffcea2c959ea758f2765fec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4f66d2e18d0c227f42d49d4238837f.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() |
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3卷引用:江苏省南京市第一中学2022届高三上学期10月阶段性检测(三)数学试题
名校
解题方法
4 . 复数
满足
,①
;②
;③复数
的虚部为
;④
是方程
在复数范围内的一个解.则以上四个结论中正确序号为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5bf0ee9e45490fb6503cc88f58d9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145e6e8cb3f167d16cdeabd3bd17ca12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369d595329752492349210d55544d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/396df1e2e35bf3040082cbb783314e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467354a996bf765789a18542f1beb008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fc19c302085de8a90e2827c32f15e7.png)
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2卷引用:天津市西青区2020-2021学年高一下学期期末数学试题
5 . 下列命题正确的是( )
A.若复数![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.![]() ![]() |
D.“复数![]() ![]() |
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名校
解题方法
6 . 设复数
对应的向量分别是
、
,则下列判断中,不正确的个数是( )
① 复数
对应的向量是
② 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6812f9cd174c662e3f98cd9eee376083.png)
③ 若向量
、
的夹角为
,则
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92374cc06be165ccd58034325b9a5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
① 复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b91254db5ff748150f449c5cdd256c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07938b3394b737e4e763f196e817ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6812f9cd174c662e3f98cd9eee376083.png)
③ 若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c2ceddeccaac02f35dbacbccb626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92374cc06be165ccd58034325b9a5df.png)
A.1 | B.2 | C.3 | D.4 |
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7 . 已知复数
满足
,
是关于
的方程
的一个根,求方程的另一个根和
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf99dd995e661caed3dc2a8583bd84e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9dc4a5491736a83a83ad9acbaf791d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25501c409bd9be522bd466352d6e20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc0837fa590b48d9719dd38ac31a9bc.png)
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名校
8 . 设a∈C,a≠0,化简:
=______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552d6430dad0932fd13525bb10488dc9.png)
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|
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3卷引用:上海市徐汇中学2020-2021学年高二上学期期末数学试题
上海市徐汇中学2020-2021学年高二上学期期末数学试题(已下线)2020年高考天津数学高考真题变式题6-10题5.2复数的四则运算 测试卷-2022-2023学年高一数学北师大版(2019)必修第二册
21-22高二上·海南·期中
9 . 关于复数
说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5d00ceb140c0d53b9e7082437f0d16.png)
A.![]() | B.![]() | C.![]() ![]() | D.![]() ![]() |
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2021·全国·模拟预测
10 . 欧拉公式被称为世界上最完美的公式,欧拉公式又称为欧拉定理,是用在复分析领域的公式,欧拉公式将三角函数与复数指数函数相关联,即
(
).根据欧拉公式,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5aa584db159b0f9bfae801d0134393b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae470980d6e3b53c65b9d42d1f011c5.png)
A.对任意的![]() ![]() |
B.![]() |
C.![]() ![]() |
D.![]() ![]() |
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