Question

f(z)=x^2-iy 复变函数的解析

Answer 1

f(z)=u(x,y)+iv(x,y),现在u=u(x,y)=x²,v=v(x,y)=-y,分别对 u,v求偏导数,则∂u/∂x=2x,∂u/∂y=0,∂v/∂x==0,∂v/∂y=-1,所以在x=-1/2函数偏导数连续且满足哥西黎曼条件:∂u/∂x=∂v/∂y,∂u/∂y=-∂v/∂x.故f(z)在x=-1/2解析.