复变函数问题,设f(x)=y^3-3x^2y+i(x^3-3xy^2),求f'(i)=
问题描述:
复变函数问题,设f(x)=y^3-3x^2y+i(x^3-3xy^2),求f'(i)=
答
f(z)=(y-ix)^3=i(x+yi)^3=iz^3
f'(z)=3iz^2
f'(i)=3i(i)^2=-3i