复数高考题型归类.pdf

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1、复数高考题型归类解析一、基本运算型二、基本概念型三、复数相等型四、复数的几何意义型练习：1.如果复数z=1+ai 满足条件|z|2，那么实数 a 的取值范围是?A.2 2,22 B.（-2，2）C.（-1，1）D.3,32.在平行四边形OABC中，顶点O，A，C分别表示 0,3 2i，24i.则对角线CA所表示的复数的模为；3.已知复数z1i(1 i)2，|z|1，则|zz1|的取值范围是；五、技巧运算型六、知识交汇型七、轨迹方程型练习：1.已知复数z满足|z|22|z|30，则复数z对应点的轨迹是()A.1 个圆 B.线段 C.2个点 D.2个圆2.如果复数z满足|z2i|z2i|4，那么|

2、zi 1|的最小值是()A.1 B.2 C.2 D.53.若|z2|z2|，则|z 1|的最小值是 .复数高考题型归类解析一、基本运算型二、基本概念型三、复数相等型四、复数的几何意义型练习：1.如果复数z=1+ai 满足条件|z|2，那么实数 a 的取值范围是?A.2 2,22 B.（-2，2）C.（-1，1）D.3,32.在平行四边形OABC中，顶点O，A，C分别表示 0,3 2i，24i.则对角线CA所表示的复数的模为；3.已知复数z1i(1 i)2，|z|1，则|zz1|的最大值.五、技巧运算型六、知识交汇型七、轨迹方程型已知复数z满足|z|22|z|30，则复数z对应点的轨迹是()A.

3、1 个圆B.线段C.2 个点D.2 个圆答案A解析由题意可知(|z|3)(|z|1)0，即|z|3 或|z|1.|z|0，|z|3.复数z对应的轨迹是1 个圆.5.如果复数z满足|z2i|z2i|4，那么|zi 1|的最小值是()A.1 B.2C.2 D.5答案A解析设复数 2i,2i，(1 i)在复平面内对应的点分别为Z1，Z2，Z3，因为|z2i|z2i|4，Z1Z24，所以复数z的几何意义为线段Z1Z2，如图所示，问题转化为：动点Z在线段Z1Z2上移动，求ZZ3的最小值.因此作Z3Z0Z1Z2于Z0，则Z3与Z0的距离即为所求的最小值，Z0Z31.故选 A.8.若|z2|z2|，则|z1

4、|的最小值是 .答案1解析由|z2|z2|，知z对应点的轨迹是到(2,0)与到(2,0)距离相等的点，即虚轴.|z 1|表 示z对 应 的 点 与(1,0)的 距离.|z1|min1.12.集合Mz|z1|1，zC，Nz|z1i|z2|，zC，集合PMN.(1)指出集合P在复平面上所表示的图形；(2)求集合P中复数模的最大值和最小值.解(1)由|z1|1 可知，集合M在复平面内所对应的点集是以点E(1,0)为圆心，以1为半径的圆的内部及边界；由|z1i|z2|可知，集合N在复平面内所对应点集是以点(1,1)和(2,0)为端点的线段的垂直平分线l，因此集合P是圆面截直线l所得的一条线段AB，如图

5、所示.(2)圆的方程为x2y22x0，直线l的方程为yx1.文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4

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7、4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3

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12、x0，yx1得A(222，22)，B(222，22).|OA|22，|OB|22.点O到直线l的距离为22，且过O向l作垂线，垂足在线段BE上，2222.集合P中复数模的最大值为22，最小值为22.文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5 ZT7Y1A10U10Y6文档编码:CT6B3B4M6Q6 HG6A8M10U3U5

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