Question

已知u-v=x^2-y^2,试求解析函数f(z)=u+iv

Answer 1

u'x-v'x=2x
u'y-v'y=-2y
因为解析,u'x=v'y,u'y=-v'x
u'x=x+y=v'y
u'y=x-y=-v'x
u=0.5x^2+xy-0.5y^2
v=0.5y^2+xy-0.5x^2