1 . 高中教材必修第二册选学内容中指出:设复数
对应复平面内的点
,设
,
,则任何一个复数
都可以表示成:
的形式,这种形式叫做复数三角形式,其中
是复数
的模,
称为复数
的辐角,若
,则
称为复数
的辐角主值,记为
.复数有以下三角形式的运算法则:若
,则:
,特别地,如果
,那么
,这个结论叫做棣莫弗定理.请运用上述知识和结论解答下面的问题:
(1)求复数
,
的模
和辐角主值
(用
表示);
(2)设
,
,若存在
满足
,那么这样的
有多少个?
(3)求和:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1116c1a2be36c2952f3f621854433824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983fa8f4d178a0a909226523a33d521c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437f03842c607c5554d86177ce090def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eec3e684af41f9ed4db5b931b9ccfb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f56cfb41ee7cb758fee138ab09e0d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30cac4804764e9ffa2a2c9c37e450713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6481f56ecdb2488e91835028d3cc7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b604ddba45cd6dbf1b937f9db82906d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77476f0974841f574785fc9940b2f8ca.png)
(1)求复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042b282f488b75517fb269e8b2512125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1d604600d084879cf3199cd0282345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce48af55c99256efdc68fac0767d944c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f56cfb41ee7cb758fee138ab09e0d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3b1a317184018ea9efc8154a878658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388d3d213a231cccf854a29eef611d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffae22ae38d7238130e81a9e554d94b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)求和:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f152097ab61600de85e8181d056dab9b.png)
您最近一年使用:0次
2024-06-12更新
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2卷引用:福建省安溪铭选中学2023-2024学年高一下学期6月份质量检测数学试题
名校
2 . 我们知道复数有三角形式,
,其中
为复数的模,
为辐角主值.由复数的三角形式可得出,若
,
,则
.其几何意义是把向量
绕点
按逆时针方向旋转角
(如果
,就要把
绕点
按顺时针方向旋转角
),再把它的模变为原来的
倍.
已知圆
半径为1,圆
的内接正方形
的四个顶点均在圆
上运动,建立如图所示坐标系,设
点所对应的复数为
,
点所对应的复数为
,
点所对应的复数为
,
点所对应的复数为
.
,求出
,
;
(2)如图,若
,以
为边作等边
,且
在
上方.
(ⅰ)求线段
长度的最小值;
(ⅱ)若
(
,
),求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8865c033cf9f1652c22297f8669623a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5ff0388004b8b37c9eeaef46a27325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5e350620ff7aab6fefc18b88573c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9979e52e407b34b82c2f7a6788743feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30deb1f343048675b9b231620369668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d442c6f979cd09bb7f8acf01d70130fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1cd5637ee5adad7e0376422ed181edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba62723e05ce6cce4d089d8b201fa857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b29a77cfdb8d2a0b684389921e1496c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2120c2838188e2affa317160f24251f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
(2)如图,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96499747e4aea990f4b878eea8d73ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499b1f470978c4f8cc05ffdebc2e961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
(ⅰ)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895928688d7557d94ccafa7ad073edfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2357ed8dbe6d3911738b8f747d670d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
您最近一年使用:0次
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613次组卷
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3卷引用:贵州省毕节市赫章县乌蒙山学校教育集团2023-2024学年高一下学期5月联考数学试题
贵州省毕节市赫章县乌蒙山学校教育集团2023-2024学年高一下学期5月联考数学试题重庆市南开中学校2023-2024学年高一下学期期中考试数学试题(已下线)5.3复数的三角形式-【帮课堂】(北师大版2019必修第二册)
解题方法
3 . 记复数的一个构造:从数集
中随机取出2个不同的数作为复数的实部和虚部.重复
次这样的构造,可得到
个复数,将它们的乘积记为
.已知复数具有运算性质:
,其中
.
(1)当
时,记
的取值为
,求
的分布列;
(2)当
时,求满足
的概率;
(3)求
的概率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57640b1fd3198b4923c61a7c5fb53c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6772d33e3e6b46834bfa6710d31d2f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e9c3910f721303685d56a8aeaccec2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080bca5fd0f1ac5d834074b3e00f92bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf2903ee65254ac0df06c3171cfec4f.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da7a625440c113848a5d7ad526d153c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
您最近一年使用:0次
名校
解题方法
4 . 已知复数
,其中
.
(1)当
时,
表示实数;当
时,
表示纯虚数.求
的值.
(2)复数
的长度记作
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4120340c64dfa74b75225caaefc9d143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef001eeef468ca21ac0cbb23fd135657.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c54258755a1798a586a77765e2b0066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad3c1424841f905de42b18326f9acfa.png)
(2)复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c042c0c7e253a65f770583c5c6696770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c042c0c7e253a65f770583c5c6696770.png)
您最近一年使用:0次
2023-08-07更新
|
308次组卷
|
5卷引用:重庆市乌江新高考协作体2023-2024学年高一下学期第一阶段学业质量联合调研抽测(4月)数学试题
重庆市乌江新高考协作体2023-2024学年高一下学期第一阶段学业质量联合调研抽测(4月)数学试题山东省泰安肥城市2022-2023学年高一下学期期中考试数学试题(已下线)第02讲 7.1.2 复数的几何意义(2 )-【帮课堂】(人教A版2019必修第二册)(已下线)7.1.2复数的几何意义【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)10.1.2 复数的几何意义-【帮课堂】(人教B版2019必修第四册)
名校
5 . 设
是一个关于复数z的表达式,若
(其中x,y,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b1cee5ac65b4e32cb0fb9e5ba4da6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
为虚数单位),就称f将点
“f对应”到点
.例如
将点
“f对应”到点
.
(1)若
点
“f对应”到点
,点
“f对应”到点
,求点
、
的坐标;
(2)设常数
,
,若直线l:
,
,是否存在一个有序实数对
,使得直线l上的任意一点
“对应”到点
后,点Q仍在直线
上?若存在,试求出所有的有序实数对
;若不存在,请说明理由;
(3)设常数
,
,集合
且
和
且
,若
满足:①对于集合D中的任意一个元素z,都有
;②对于集合A中的任意一个元素
,都存在集合D中的元素z使得
.请写出满足条件的一个有序实数对
,并论证此时的
满足条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c01e03a93ade8659780af659f12e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5bbd08209bda97df3e33163556561e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b1cee5ac65b4e32cb0fb9e5ba4da6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30096b7bfb7d8e94336df5d1f92f16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969b9043717a5b07402958abc5749290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b40590fd0945eb5c688d64e0a8d9f3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f669a1d6376f795f05b47eb7d8067c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2692896964f98fc258f795c0be6dd35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)设常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96f5020aef5aef03ec7f406460f608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649546dd164eaac1f5f77a20293899c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b9dfb28a818d4435d04c101174bbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30096b7bfb7d8e94336df5d1f92f16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b9dfb28a818d4435d04c101174bbbb.png)
(3)设常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c471126f22232a1ff1e88591bde0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3473c334445af65176dde2d2e5d890ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0054d6123e214792c699c3ec1a1f8fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9f9cebf7c3111773f43f0be6510148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3ac8e9f3746c0993b1f1d31620fec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70b34fa2acd6a5c2e2e37222d58ec68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2527414d896f7af69a7a620e1cc57676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c01e03a93ade8659780af659f12e09.png)
您最近一年使用:0次
2023-07-05更新
|
1045次组卷
|
11卷引用:上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题
上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题江苏省泰兴中学、泰州中学2023-2024学年高一下学期5月联合质量检测数学试卷上海市控江中学2022-2023学年高一下学期期末数学试题(已下线)专题01 条件开放型【练】【通用版】湖南省邵阳市第二中学2024届高三下学期入学测试数学试题(已下线)高一下学期期中数学试卷(提高篇)-举一反三系列浙江省绍兴市第一中学2023-2024学年高一平行班下学期期中考试数学试卷(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)(已下线)专题03 复数-《期末真题分类汇编》(人教A版2019必修第二册)(已下线)复数-综合测试卷A卷广东省惠州市博罗县2023-2024学年高一下学期5月期中考试数学试题
名校
6 . 在英语中,实数是Real Quantity,一般取Real的前两个字母“Re”表示一个复数的实部;虚数是Imaginary Quantity,一般取Imaginary的前两个字母“Im”表示一个复数的虚部.如:
,
;
,
.已知复数z是方程
的解.
(1)若
,且
(a,
,i是虚数单位),求
;
(2)若
,复数
,
,且
,
,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2feba771ef35780fd3730a7f64e92af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f180e675d09eb3f38d45b5178fda797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03f55ee5dd80c3d6c4993bf2b4bfe9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be07a99ddc4d937071dd7b68a25f6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0d4d254ff83c9298b1eecb3b4c831c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6aecd620e40fe87a8ad3230bc91deaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4111b5bb1c41cc93d75f29a9539afd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d165b3397aab477869842a16b7ff6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff0f1b6dd0be54207299f6c22eec25f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b896385877f1431f7cb6039c6d4e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee3a3acbc491caa282b95be84300be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476d332663b8fc357c1a3fc85f9fa5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f07c0d81d401253c3a9d48c9428a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d3e597e6175d602094521e85d58e99.png)
您最近一年使用:0次
2023-04-14更新
|
261次组卷
|
3卷引用:河北省南宫中学2022-2023学年高一下学期第二次月考数学试题
名校
7 . 已知复数
,集合
,集合
,
(1)若
使得
(
为虚单位),求
的最小值;
(2)若当
时,集合
有两个子集.
①求
的取值范围;
②求集合
中复数
对应点
形成的复平面区域的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51e2164fb8db54bbc974c937119f1d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a720a4f314efcf8aacedf407334197f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2129600c6623c8b81c47151440ea9ddd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010e6bdfd73b146e42df3f899513183c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5f6c6c2d42b75cffc3c4adcad1edc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad053ae69ea1b0e01aa7e8a93aca3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c450aa751cacd6442e82062d4b8b1e9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c64b75adfa934653fb3447a898f3fde.png)
②求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
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名校
解题方法
8 . 设
,
均为复数,在复平面内,已知
对应的点的坐标为
,且
对应的点在第一象限.
(1)若复数
为纯虚数,求实数m的值;
(2)若
,且
是关于x的方程
的一个复数根,求
.
![](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/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4040b5acf7414fd72197ed4cb0a9360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
(1)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686969f59776c14bf1e0ee97425db9a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a2b6f6e42f7450bda37dd01705428d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e965699dc5f10adcb871cfdf0bbbc6c.png)
您最近一年使用:0次
2022-06-13更新
|
818次组卷
|
4卷引用:山东省菏泽市思源学校2023-2024学年高一下学期数学第一次月考(4月)数学试题
山东省菏泽市思源学校2023-2024学年高一下学期数学第一次月考(4月)数学试题山东省临沂市莒南县2021-2022学年高一下学期期中数学试题(已下线)第05练 复数-2022年【暑假分层作业】高一数学(苏教版2019必修第二册)江苏省苏州中学2022-2023学年高一下学期期中数学试题
名校
9 . 在复平面内,复数
表示的点
,求出满足下列条件的复数
.
(1)若点
在虚轴上,求复数
的共轭复数
;
(2)若点
在直线
上,求复数
的模
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f46110fae083d4ce620e88ce4079844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
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名校
解题方法
10 . 已知向量
与实轴正向的夹角为
,向量
对应的复数
的模为1,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d850c2157b5355cb1c718b4577483cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d850c2157b5355cb1c718b4577483cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
您最近一年使用:0次