复变函数期中考试试题.pdf
优秀学习资料欢迎下载曲 靖 师 范 学 院20112012学年度上学期信息与计算科学专业20091121班复变函数期中考试试卷任课教师：负责人：(签字)题 号一二三四总 分复核人分 值24 24 32 20 100 得 分登分人注意：1.本试卷共8 页，请考生注意检查，有错、漏、破烂请及时报告监考教师更换。2.考生班级、学号和姓名必须写在指定地点。3.考试形式：闭卷；考试时间：120 分钟。一、单项选择题（共8 小题，每小题 3 分，满分 24 分）1.已知iz2531，iz4332，求zz3231的值为（B）.A.182-186i B.182+186i C.224-362i D.224+362i 2.iArg43的值为（A）.A.34arctan12K B.34arctan12K C.43arctan12K D.43arctan12K3.复数有多种表示形式，iz3 的指数形式为（AD）.A ei23 B.ei23 C.-ei23 D.ei234.关于聚点的说法0z为 E 的聚点或极限点0z的任一邻域内含有 E 的无穷多个点0z的任一邻域内含有异于0z而属于E的一个点得分阅卷人班级_学号_姓名_-密-封-线-第 1 页，共 5 页精品p d f 资料 可编辑资料-优秀学习资料欢迎下载可从 E 中取出点列12,nz zz，以0z为极限以上说法中等价的是（D）.A.B.C.D.5.下列函数处处连续，又处处不可微的是(B).Aze B.zC.sin z D.21z6.计算dziz2222的值为（D）.A.32i B.32i C.3i D.3i7.设函数 fz 在z平面上的单连通区域D 内解析,则（C）.A.若 C 为 D 内任一周线时,有0Cfz dz,而若 C 为 D 内任一闭曲线时,不一定有0Cfz dz.B.fz 在 D 内积分与路径有关.C.则函数0zzF zfd0,zD zD 在 D 内解析，且Fzfz.D.则函数02zzF zfd0,zD zD 在 D 内解析，且Fzfz.8.下列论断正确的是（D）.A.复数都能比较大小.B.复数都有辐角.C.sin1z，z是任意的复数.D.区域必为开集.二、填空题（共 8 小题，每小题 3 分，满分 24 分）1.3i得分阅卷人-第 2 页，共 5 页精品p d f 资料 可编辑资料-文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2优秀学习资料欢迎下载2.131izii的共轭复数为 .3.设13Zi，则 z 2 ,arg z _,z _.4.函数 sin z的周期为 _ 2_.5.若函数zf在整个平面上处处解析，则称它是整函数 .6.ixyizfyyxx322333,则()fz=.7.积分3zCze dz(C 为单位圆)的值为 .8.命 C表示连接点 a 及 b 的任一曲线，则dzzC .三、解答题（共 4 小题，每小题 8 分，满分 32 分）1.求复数11zz的实部和虚部2.将复数sincos1i0化为指数形式.3.判断下列函数的可微性和解析性：（1）、izfyx22;（2）、izfyx2232得分阅卷人-第 3 页，共 5 页精品p d f 资料 可编辑资料-文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2优秀学习资料欢迎下载4.计算积分：CzdzRe，这里的 C表示连接原点到的i1直线段.解：连接 O 及 1+i 的直线段的参数方程为：z=（1+i）t（0t1）,故21)1 ()1 R e (Re10idtitizdzC=（1+i）10tdt=21i四、证明题（共 2 小题，每小题 10 分，满分 20 分）1.证明方程ttiz22是什么曲线.证明：2.试证明22Czdz.积分路径 C是连接 i 和i2的直线段.得分阅卷人-第 4 页，共 5 页精品p d f 资料 可编辑资料-文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 HB4L8H5Z3S6 ZX9Y1I3T7U2文档编码:CK7X4R5M8M3 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