1 . 已知函数
,其中
,证明:存在
,且
.
的根的实部全部大于0.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b748237d3ad510f872cb96097e0e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f016c950ab496393ba95c709cbc6e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e0c37d5595299c1886e6d812a946e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3ac8c6973c1a97dc47d4fb6737c709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7165f4d49fc207e7cdc35fccdb18e532.png)
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名校
2 . 利用平面向量的坐标表示,可以把平面向量的概念推广为坐标为复数的“复向量”,即可将有序复数对
视为一个向量,记作
.类比平面向量可以定义其运算,两个复向量
,
的数量积定义为一个复数,记作
,满足
,复向量
的模定义为
.
(1)设
,
,求复向量
,
的模;
(2)设
、
是两个复向量,证明柯西一布涅科夫斯基不等式仍成立,即:
;
(3)当
时,称复向量
与
平行.设
、
,若复向量
与
平行,求复数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20b691a717378e3d8190ae22dcfac98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05d9f656141217dfaeb5f801b6bd076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05d9f656141217dfaeb5f801b6bd076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dbf9f180aaa478d4d882ac76396204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22450b6531374303881c695c8a5620d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7b089f50046f4c1b8ab6bbf76d01a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abaee1c69773edf2ab23813457e7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265cbe9d30b58d4064180ebd00917709.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2620bbe3536336e8053dbe070bbbcda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3c44388f3506e8e7233e8e66bfed1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abaee1c69773edf2ab23813457e7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ba307b4e15fa3e07317bb750538d21.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abaee1c69773edf2ab23813457e7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ba307b4e15fa3e07317bb750538d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7814b368e7a77a4fa22b9a0a458030d1.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/038c9b64c1d13c3bc2ae0c45bb5b1bc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abaee1c69773edf2ab23813457e7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ba307b4e15fa3e07317bb750538d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e152ff599219b8a99f668fd45c087048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2371caebe89fc60f795f58db5f3db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abaee1c69773edf2ab23813457e7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ba307b4e15fa3e07317bb750538d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
您最近一年使用:0次
2021-07-12更新
|
1279次组卷
|
9卷引用:专题05 复数压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)
(已下线)专题05 复数压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)第02讲 复数的运算-【帮课堂】2021-2022学年高一数学同步精品讲义(苏教版2019必修第二册)上海交通大学附属中学2020-2021学年高一下学期期末数学试题(已下线)7.2复数的四则运算C卷第12章 复数(单元测试)-2022-2023学年高一数学同步精品课堂(苏教版2019必修第二册)高一复数重难点提高卷-【同步题型讲义】(已下线)第七章 复数(基础、典型、易错、压轴)分类专项训练(2)(已下线)复数的概念与运算(已下线)第7章 复数-《重难点题型·高分突破》(人教A版2019必修第二册)
3 . 求证:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411d0fec78c98dda7eb2e048df7d1b40.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea42cfc60639a2634a729e7a120152c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694edfed19f6c329e360bf2bef4e23d7.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4695e20874a7ce9d94c3fc1d5f4504.png)
您最近一年使用:0次
2020-01-30更新
|
1273次组卷
|
6卷引用:专题05 复数压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)
(已下线)专题05 复数压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)人教B版(2019) 必修第四册 逆袭之路 第十章 10.2.2 复数的乘法与除法(已下线)第19讲压轴综合题(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)第十章 复数 10.2 复数的运算 10.2.2 复数的乘法与除法人教B版(2019)必修第四册课本习题10.2.2 复数的乘法与除法(已下线)第七章 复数(基础、典型、易错、压轴)分类专项训练(2)
名校
4 . 设复平面上点
对应的复数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb77d49f9e0b0d2e01c2258f493b3270.png)
(
为虚数单位)满足
,点
的轨迹方程为曲线
. 双曲线
:
与曲线
有共同焦点,倾斜角为
的直线
与双曲线
的两条渐近线的交点是
、
,
,
为坐标原点.
(1)求点
的轨迹方程
;
(2)求直线
的方程;
(3)设△PQR三个顶点在曲线
上,求证:当
是△PQR重心时,△PQR的面积是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb77d49f9e0b0d2e01c2258f493b3270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93daf2cfc24f09c8474a14c9a5799cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2fd836eee4117616c00dff7a4068d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde71eaaba1444a7a965721162fa9195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](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/d3c16325e47c47fa58c4ac3b4c2c17b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设△PQR三个顶点在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2018-04-16更新
|
1085次组卷
|
4卷引用:考向30 复数-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向30 复数-备战2022年高考数学一轮复习考点微专题(上海专用)上海实验学校2022届高三冲刺模拟卷二数学试题上海市奉贤区2018届高三下学期调研测试(二模)数学试题上海市位育中学2021届高三下学期开学考试数学试题
5 . 已知
是虚数,
是实数.
(1)求
为何值时,
有最小值,并求出|
的最小值;
(2)设
,求证:
为纯虚数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ae50806d8c14f0275864b30e9f30a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ea06ebfbf9ca9c9dfea5be4d623068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ea06ebfbf9ca9c9dfea5be4d623068.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f747900f5f6a6380bdab32ccbd4642e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
您最近一年使用:0次
2017-05-21更新
|
2187次组卷
|
4卷引用:专题16 复数——常见中档题型汇编-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)
(已下线)专题16 复数——常见中档题型汇编-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)江苏省江阴市四校2016-2017学年高二下学期期中考试数学(理)试题安徽省定远重点中学2017-2018学年高二下学期教学段考数学(理)试题江苏省苏州市吴中区2018-2019学年高二下学期期中数学(理)试题