名校
1 . 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)
您最近一年使用:0次
2 . 在复平面内,复数
对应的点为
,
对应的点为
.
(1)求
.
(2)若复数z满足
,则复数z在复平面内对应的点的集合是什么图形?并判断点A与该图形的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb8c1ac253f504497962194df593bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4535188c0996ec130c8a7aaf08dc66.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe615164ed2995bdeea0f5b0ba94231.png)
(2)若复数z满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b56c5d57b748a7d5d059955de8558d1.png)
您最近一年使用:0次
2022-07-02更新
|
253次组卷
|
2卷引用:河南省安阳市2021-2022学年高一下学期期末数学试题
21-22高一·湖南·课后作业
3 . 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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名校
解题方法
4 . 在平面直角坐标系中,O为坐标原点,满足
的复数
对应的动点
的轨迹记为
.
(1)若
为双曲线,求该双曲线的焦距和a的取值范围;
(2)若
,且直线
与
交于A、B两点,求
的面积
;
(3)若
,过点
的直线
与
有且仅有一个公共点,求
与
的公共点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b19a09fd9932787f5fb61b16af7bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14ef34caabc3b029b69859580279beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb51096f4d54ad3cc2aa72a26151904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a711bf44ed64556c72fbb0e7f42c27f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
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20-21高一·全国·课后作业
5 . 设全集U=C, A={z|||z|-1|=1-|z|,z∈C},B={z||z|<1,z∈C},若z∈A∩(∁UB),求复数z在复平面内对应的点的集合.
您最近一年使用:0次
20-21高一·全国·单元测试
6 . 已知集合A={z||z|≤1},
(1)求集合A中复数z=x+yi所对应的复平面内动点坐标(x,y)满足的关系?并在复平面内画出图形.
(2)若z∈A,求|z﹣(1+i)|的最大值、最小值,并求此时的复数z
(3)若B={z||z﹣ai|≤2},且A⊆B,求实数a的取值范围.
(1)求集合A中复数z=x+yi所对应的复平面内动点坐标(x,y)满足的关系?并在复平面内画出图形.
(2)若z∈A,求|z﹣(1+i)|的最大值、最小值,并求此时的复数z
(3)若B={z||z﹣ai|≤2},且A⊆B,求实数a的取值范围.
您最近一年使用:0次
解题方法
7 . 如图,在复平面
中,平行四边形
的顶点
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/98efbf3a-d932-4a8b-95dc-4ac0ae3dda30.png?resizew=161)
(1)求点
对应的复数;
(2)记点
,
,
对应的复数分别为
,
,
.
①若
,求复数
;
②若复数
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ceec39aaaccbeaac9a4a5bdbb0f0e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f9283c71dafdd292ae615c735bcf08.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/98efbf3a-d932-4a8b-95dc-4ac0ae3dda30.png?resizew=161)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3594b3195943d5b87e4e622cf6d0640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
②若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843c531f403adf796fe8350e2f419c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af159e78033bc114e43eea9c14f62ed.png)
您最近一年使用:0次
2021-08-15更新
|
224次组卷
|
2卷引用:苏教版(2019) 必修第二册 过关斩将 期中学业水平检测
8 . 已知复平面内
点对应的复数为
,
点对应的复数为
,
.若
,在
的轨迹上任取一点
,求
的面积取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6c8c0b04eaf2d1729d63524172df97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719fe6c33d484fd599b1936b57fa4396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0663b7077ec6d9e2b7f924c06a39ef56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70c2519610d6d1d6d0855b0f27dfc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
9 . 已知向量
,在复平面坐标系中,i为虚数单位,复数
对应的点为
.
(1)求
﹔
(2)
为曲线
为
的共轭复数)上的动点,求
与
之间的最小距离;
(3)若
,求
在
上的投影向量
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6517c5d60c88f95c41cfb18c6ef62fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f1047ec4e5edaad6f95c9719f6a157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8477bcc87b1401970171bf57b9ecb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf56137f1d545c524da223f94f1c99f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0f9ba4ddaba95860c909cb28557f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8477bcc87b1401970171bf57b9ecb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6a1d319648bb969845a9159cdba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759bc4eeb0c937af667093c416ed83bc.png)
您最近一年使用:0次
2021-06-20更新
|
1026次组卷
|
7卷引用:山东省济宁市泗水县2021-2022学年高一下学期期中考试数学试题
20-21高三下·浙江·期末
解题方法
10 . 在复平面中原点为O,已知A对应的复数为
,点B对应的复数为
,
,点C对应的复数为
,且
,且B,C均在实轴上方,
(1)求
的取值范围;
(2)当
时,P是线段
上的动点,求
的取值范围;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f48d2b68f7480f35f9f2632564d1dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52bb069b71ff58af8b36823d1af6a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d2d17663db4e87a6bc187a43700924.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87e8cdf5716e8c4aa29de4d4bd6d7b6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223b6f16e1cdb3ab3d10905d7fa0a7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73de3a47976a9e064dd7e3091894acc0.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18c66c4e24d0475b2cd9ddc5e53540f.png)
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