21-22高一·湖南·课后作业
1 . 已知
中,
,
对应的复数分别为
,
,通过几何作图求出这两个复数和与差对应的向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b40e803a6dc17c94688c925db9ad8c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074e5013ee50ec72ae18230517cd3c78.png)
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解题方法
2 . 若虚数
满足
的实部与虚部互为相反数且___________,求复数
.在下列条件中任选一个填在横线上补全条件,并求解问题.①
是实数;②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95146f921154bd1fdcf411ccd8641576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bb0bfb7b8824ab33920e350082fcf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cba5b3bb49817e8c8073064b4ed744c.png)
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20-21高二·全国·假期作业
解题方法
3 . 设有下面四个命题:
①若复数
满足
,则
;
②若复数
满足
,则
是虚数;
③若复数
满足
,则
;
④若复数
、
满足
,则
;
其中是真命题的有___________ (填写所有真命题的编号).
①若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd79b4eb70d48435dec8824ad892494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70cecfc37310dd869b0d51ff44d64e9.png)
②若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452262f21f9a05d43e371fa3f5b126a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
③若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc97f70a58d22400f7ab50fa1cdc79d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70cecfc37310dd869b0d51ff44d64e9.png)
④若复数
![](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/e045c712fb1efd2b4681134707cc86c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de59a6da1ee210ccf04651ae53275dd.png)
其中是真命题的有
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4 . 在下列命题中,正确的命题有________ (填写正确的序号)
①若
,则
的最小值是6;
②如果不等式
的解集是
,那么
恒成立;
③设x,
,且
,则
的最小值是
;
④对于任意
,
恒成立,则t的取值范围是
;
⑤“
”是“复数
(
)是纯虚数”的必要非充分条件;
⑥若
,
,
,则必有
;
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef389807e5cb964f7756c6841f7161d.png)
②如果不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae8fff7c98b78992edcd61daf6ea72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7b2668d8fcf713370822c8e368ba7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da693578d4cd0c841fd529fe7ebfe4d.png)
③设x,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2519954ec2deabecd7e057886fa4023c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8887f77124cbe18a4931826ede9c9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
④对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b687f97094676b2755bc724219a58520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ce220e0583c843810d4b44de111156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49bc53d70ee599df5cad39f06f728c2.png)
⑤“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d96d22950baabd8ca6647205f1d3cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
⑥若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2e606c883dace7fbd88223c8067885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9d3040a7a1fc2cf8ac555dbafc97dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc277eef249facf647e13a58e3c2fe26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297a7062ba8f240d7517f0dd3ee6a27d.png)
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5 . 对任意复数
.
,定义
,其中
是
的共轭复数.对任意复数
.
.
,有如下四个命题:
①
;
②
;
③
; ④
.则真命题是________ (填写命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3871a062c5e0a4e009b01aa47afb48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a14b56f7f7bb23cd4bf9041e440a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6745295f16b342aa42f374ef4801c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a32fb6da4da15b115bd5eb7a8aa4d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a14b56f7f7bb23cd4bf9041e440a46.png)
![](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/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4802007201b1d464e62595a328e52e9f.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67df30bc42ff7a5697a2b7812ab8fafa.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8788f274707335caf1f687c2d54d65a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7adda3b160661900e75f666061a84e67.png)
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2017-06-17更新
|
903次组卷
|
2卷引用:上海市复旦大学附属中学2021-2022学年高二上学期期末数学试题
6 . 把下列复数表示成三角形式,并画出与之对应的向量.
(1)6;
(2)
;
(3)
;
(4)
.
(1)6;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186bb9626ba707655b540871c863bdc4.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2827c919b6fc736f610fd8f03ad1ce.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c9adfb7e33153f1234be52e296355a.png)
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2022-08-19更新
|
392次组卷
|
7卷引用:苏教版(2019) 必修第二册 过关斩将 第12章 12.4 复数的三角形式
苏教版(2019) 必修第二册 过关斩将 第12章 12.4 复数的三角形式复数的三角表示(已下线)7.3.1复数的三角表示式(精讲)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)专题7.6 复数的三角表示(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)第03讲 复数的三角表示-《知识解读·题型专练》(人教A版2019必修第二册)(已下线)专题7.5 复数全章九大基础题型归纳(基础篇)-举一反三系列-(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)
21-22高一·湖南·课后作业
7 . 设
,
,建立复平面并画出满足条件的点构成的图形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707aed47159fae11f47e464c548a0b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ad21e902bd86cafb33d190c5f689f5.png)
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8 . 一般地,任何一个复数
(
,
)都可以表示成
形式,其中,
是复数
的模,
是以
轴的非负半轴为始边,向量
所在射线(射线
)为终边的角,叫做复数
的辐角,
叫做复数
的三角表示式,简称三角形式.为了与“三角形式”区分开来,
(
,
)叫做复数的代数表示式,简称“代数形式”.
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854509800087552/2854700911837184/STEM/9fa61714-64b7-42d8-93cd-0fdc75ca7c50.png?resizew=259)
(1)画出复数
对应的向量,并把
表示成三角形式;
(2)已知
,
,
,其中
,
.试求
(结果表示代数形式).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6b88af810dbab3e7a0e9baeafb15f1.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2065e8d7f0afb35f64ea5fbea3c400f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54d290009e138d1f0d4cb771cada9f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6b88af810dbab3e7a0e9baeafb15f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eed3d568acf369a315c7ab41c081049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854509800087552/2854700911837184/STEM/9fa61714-64b7-42d8-93cd-0fdc75ca7c50.png?resizew=259)
(1)画出复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc933d8e17ad3edfe04a3d4a2d0716d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc933d8e17ad3edfe04a3d4a2d0716d.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/156ca68a083a7bcd5f68def3a0c6819d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c0a7c890678066124a9e121b3c3ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1c7ea09ace27da0f06903c7c0f333a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0219728a25d5ab029d733f699b91b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef51ef02d31f879e9534ea019b4f8aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da4e6752d8c8a0705194f2b2f16ab5d.png)
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2021-11-19更新
|
804次组卷
|
10卷引用:热点06 平面向量、复数-2022年高考数学【热点·重点·难点】专练(新高考专用)
(已下线)热点06 平面向量、复数-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)考点56 数系的扩充与复数的引入-备战2022年高考数学典型试题解读与变式(已下线)7.3 复数的三角表示(已下线)专题04 复数基础题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)专题5.3 复数(能力提升卷)-2021-2022学年高一数学北师大版2019必修第二册山东省济宁邹城市2021-2022学年高三上学期期中考试数学试题(已下线)7.3复数的三角表示A卷(已下线)12.4 复数的三角形式-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(苏教版2019必修第二册)(已下线)专题7.6 复数的三角表示(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)广东省佛山市顺德区华侨中学(港澳班)等学校2024届高三下学期3月联考数学试题