设x*x+axy+by*y+i（cx*x+dxy+y*y）的解析函数,求解,求解啊,大神,学霸门!

Question

设x*x+axy+by*y+i（cx*x+dxy+y*y）的解析函数,求解,求解啊,大神,学霸门!

Answer 1

u=x^2+axy+by^2
v=cx^2+dxy+y^2
由轲西黎曼公式：
u'x=2x+ay=v'y=dx+2y,对比系数得：d=2,a=2
u'y=ax+2by=-v'x=-2cx-dy,对比系数：a=-2c,2b=-d,解得：c=-1,b=-1
因此解析函数为
x^2+2xy-y^2+i(-x^2+2xy+y^2)
=(x+iy)^2-i(x+iy)^2
=(1-i)z^2