文档介绍：复变函数模拟试题试题(五)(每空3分,共15分)),2)(32(iiz?????,)1(51)(3zizxf???则方程0)('?,1|4|??z则?????)4()(1izz?在?????||,12)(2zzzf??]),([Re??(每题3分,共15分),不是圆周的为().(A),221???zz(B),4|3|3????Zz(C))1|(|,11????aazaz(D)),0(,0??????)(zf在区域D内有定义,则下命题中,正确的是()(A)若|)(|zf在区域D内是一常数,则)(zf在D内是一常数.(B)若))(Re(zf在区域D内是一常数,则)(zf在D内是一常数.(C)若)(zf与)(zf在区域D内是解析,则)(zf在D内是一常数.(D)若)(argzf在区域D内是一常数,则)(,2||?z则???cdzzz).()1(cos2(A)1sin?(B)1sin(C)1sin2i??(D)1sin2i?)(zf在圆环域201||:RzzRH???内的罗朗展开式为???????nnnzzc,)(0C为H内饶0z的任一条正向简单闭曲线,那么???cdzzzzf)()()(20(A)12?ic?(B)21ic?(C)22ic?(D))('20zif??为解析函数)(zf的m级零点,则).(],)()('[Re?azfzfs(A)m,(B)m?(C)1?m(D))1(??m三.(10分)设,0?a在复数集C中解方程.||22azz??四.(10分)讨论函数???????????0,00,))(()(4222zzyxixyyxxzf在原点0?.(10分)将函数)1()2ln()(2???zzzzf在1|1|0???.(10分)求积分,||dzzezz??从而证明???????0cos.)cos(sinde七.(10分)求分式线性变换),(z?使1||?z映射为,1||??且使iz??1,1映射为.,1???八.(10分)试证明?????????????1||2!)]1(2[)12(221znnnnnnizdzzz??.九.(10分)计算积分??????0222).0,0()(sinamdxaxmxx复变函数模拟试题试题(五)??,2,1,0,424sin424cos28????????????????kkik?????104.??????02)()1(nnnnizi(5)-.(B)2.(C)3.(C)4(B)5.(A):令,iyxz??则方程等价于ayxxyiyx?????222222比较两边的实部与虚部,得????????ayxyxxy2222202即???????ayyx||202或??????axxy||)1|(|2ay