Question

一个习题里面有这样的：.w=y^3-3yx^2+i(x^3-3xy^3+c)化为w=f(z)=i(z^3+c)请问是怎么

Answer 1

这应该有个前提条件是 z = x + iy 吧

w = y^3-3yx^2+i(x^3-3xy^3+c) = y^3 - 3(ix)y^2 + 3(ix)^2 y - (ix)^3 + ic

= (y - ix)^3 + ic = (-i(x + iy))^3 + ic = (-iz)^3 + ic

= iz^3 + ic = i(z^3 + c)