复数计算练习题.pdf

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1、一、选择题(本大题共 12小题，每小题 5 分，共 60 分，在每小题给出的四个选项中，只有一项是符合题目要求的)1已知 a，bR，则 ab 是(ab)(ab)i 为纯虚数的()A充要条件B充分不必要条件C 必要不充分条件D既不充分也不必要条件答案C2.10i2i()A24i B24iC 24i D24i答案A3若 w1232i，则 w4w21 等于()A1 B0C 33i D13i答案B4在(1232i)12的展开式中，所有奇数项的和等于()A1 B1C 0 Di答案B5已知z1i2i，则复数 z()A13i B13iC 3i D3i答案B解析z1i2i，z(2i)(1 i)23i i213

2、i.z13i.6复数2i1i2等于()A4i B4iC 2i D2i答案C7复数?22i?4?13i?5等于()A13i B13iC 13i D13i答案B8复数 12i3()A12i B12iC 1 D3答案A解析12i312i12i，故选 A.9在复数集 C内分解因式 2x24x5 等于()A(x13i)(x13i)B(2x23i)(2x23i)C 2(x1i)(x1i)D 2(x1i)(x1i)答案B10复数 i3(1 i)2()A2 B2C 2i D2i答案A解析由题意得 i3(1 i)2i 2i 2i22，选 A.11复数 z11i的共轭复数是()A.1212i B.1212iC 1

3、i D1i答案B解析z11i1i?1i?1 i?1212i，z1212i，故选 B.12已知复数 z1i，则z22zz1()A2i B2i文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ

4、3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T

5、7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ

6、3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T

7、7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ

8、3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T

9、7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8C 2 D2答案B二、填空题(本大题共 4小题，每小题 5 分，共 20 分把答案填在题中横线上)13已知复数 z2i，则 z44z36z24z1_.答案6解析z44z36z24z1(z44z36z24z1)2(z1)42

10、(1 i)42(1 i)222(2i)22426.14i4 ni4 n1i4 n2i4 n3_(n 为正整数)答案015已知?1i?31ia3i，则 a_.答案23i16设 zC，z|z|2i，则 z_.答案34i解析设 zabi，则|z|a2b2.abi a2b22i.aa2b22，b1.a34，b1，z34i.三、解答题(本大题共 6小题，共 70 分，解答应出写文字说明、证明过程或演算步骤)17(10 分)若复数 zm2m 2(2m2m 3)i(m R)的共轭复数 z 对应的点在第一象限，求实数 m的集合解析由题意得 z m2m 2(2m2m 3)i.m2m 20，?2m2m 3?0，即

11、m2m 20，2m2m 30，解得 1m 32.文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4

12、M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3

13、 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4

14、M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3

15、 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4

16、M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3

17、 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U818(12 分)计算(1232i)3.解析方法一(1232i)3(1232i)2(1232i)(1232i)(1232i)(32i)2(12)234141.方法二原式(12)33(12)232i 312(32i)2(32i)318338i 98338i 1.19(12 分)已知复平面内点 A、B对应的复数分别是

18、z1sin2i，z2cos2icos2，其中(0,2)，设 AB对应的复数为 z.(1)求复数 z；(2)若复数 z 对应的点 P在直线 y12x 上，求 的值解析(1)zz2z1cos2sin2i(cos2 1)1i(2sin2)(2)点 P的坐标为(1，2sin2)由点 P在直线 y12x，得 2sin212.sin214，sin 12.又(0,2)，6，56，76，116.20(12 分)已知复数 z?1i?2 3?1i?2i，若 z2azb1i，试求实数 a、b 的值解析化简得z1i代入方程，得ab(2a)i 1i.ab1，2a1，a3，b4.21(12 分)设 z(a2a6)a22a

19、15a24i(aR)，试判断复数 z 能否为纯虚数？并说明理由解析假设复数 z 能为纯虚数，则a2a60，a22a15a240.a3或a2，a5且a3且a2.文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V

20、6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文

21、档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V

22、6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文

23、档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V

24、6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文

25、档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8不存在 a 使复数 z 为纯虚数22(12 分)已知 aR，问复数 z(a22a4)(a22a2)i所对应的点在第几象限？复数z 对应点的轨迹是什么？解析由 a22a4(a1)233，(a22a2)(a

26、1)21 1，得 z 的实部为正数，z 的虚部为负数复数 z 对应的点在第四象限设 zxyi(x，yR)，则xa22a4，y?a22a2?.消去 a22a，得 yx2(x3)复数 z 对应点的轨迹是一条射线，其方程为 yx2(x3)文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5

27、P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码

28、:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5

29、P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码

30、:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5

31、P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8文档编码:CC7E7T7T9V3 HN4V6Q5P3N3 ZZ3C9R4M7U8