名校
1 . 若
,则
的虚部为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600671a4d22a5a932b866304ebc69792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
A.![]() | B.1 | C.3 | D.![]() |
您最近一年使用:0次
名校
2 . 若
为复数,
,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be94c746ea0cb4834e5295672e229a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ef14d1e3d28b47cd21e21c991509e4.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() ![]() |
您最近一年使用:0次
2024-06-03更新
|
376次组卷
|
2卷引用:黑龙江省牡丹江市第一高级中学2023-2024学年高一下学期期中考试数学试题
名校
3 . 设复数
,
.
(1)若
是纯虚数,求
的值;
(2)若复数
在复平面内对应的点在第四象限,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1988e53b17687a87e751e9513c20a0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4ddcdc131d6f0a1f17d637b1179f77.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34b88f343ca5a4c29057465541b9cf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7be74b3741e5b47713ed3ce08398f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
4 . 设复数
,其在复平面内对应点为
,且
,复数
,其在复平面内对应点为
,且
,若存在
的轨迹上的两点
、
,使
,则
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f41acaa456df1ac6e5af4fc056f780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c69a18ac82d772e7c7707efe8f44eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72aeab648917f787ddb15d9039b8856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e380c51ad6d645900156ff061992799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42143191548a417aa602e2f884df244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
5 . 若复数
满足
(其中
是虚数单位),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0a76f74b83ef030c25a484ade0bc0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
A.![]() ![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 设
,
,则a等于________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf825efc71d548c3e5f23ada63fbcc69.png)
您最近一年使用:0次
名校
7 . 我们可以把平面向量坐标的概念推广为“复向量”,即可将有序复数对
视为一个向量,记作
.类比平面向量的线性运算可以定义复向量的线性运算;两个复向量
,
的数量积记作
,定义为
;复向量
的模定义为
.
(1)设
,
,求复向量
与
的模;
(2)已知对任意的实向量
与
,都有
,当且仅当
与
平行时取等号;
①求证:对任意实数a,b,c,d,不等式
成立,并写出此不等式的取等条件;
②求证:对任意两个复向量
与
,不等式
仍然成立;
(3)当
时,称复向量
与
平行.设
,
,
,若复向量
与
平行,求复数z的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20b691a717378e3d8190ae22dcfac98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2adcabafb9c785403537056956f8ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2adcabafb9c785403537056956f8ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f78ec4dc660466c71c79c688f8bbf49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc49dd09fc7dda38a4de6ad364580512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21a8efc21764c68641ca8a870cff10f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb467f8f90ba3c6ed8dcd5e9b385c5c0.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb5d6f118bc0f8ca3f73d3c2e93804f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e46d773a664a544127aae7eb8374e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
(2)已知对任意的实向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7f2b6e510313331fd7c781e3837b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
①求证:对任意实数a,b,c,d,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a8f3b9c67bee7fd6b1312a57a6795a.png)
②求证:对任意两个复向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7f2b6e510313331fd7c781e3837b37.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66114f41d0e72a29cd584844a432f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4e71ddc3533ffdeb7c4feb9ac23099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47066ed3effe45f5e5d9fd9fc1faa2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707aed47159fae11f47e464c548a0b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
您最近一年使用:0次
名校
8 . 已知
与
是共轭虚数,以下四个命题一定正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
9 . 若复数
满足
,则
( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe74b48570b75521a6b16f12d0e80bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
10 . 已知复数
满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0967cd74304eaf3bead33d641cfa416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-08更新
|
1554次组卷
|
7卷引用:黑龙江省大庆市大庆中学2023-2024学年高一下学期5月期中考试数学试题