let f(z) = u +iv, z = x +iy

let u and v be defined as follows:

u(x,y) = (x^3 - y^3) / (x^2 + y^2) if (x,y)≠(0,0), u(0,0)=0

v(x,y) = (x^3 + y^3) / (x^2 + y^2) if (x,y)≠(0,0), v(0,0)=0

solve lim [f(z) - f(c)] / (z-c) as z approaches c. that is, show f'(c) exists

our instructor told us a hint: solve it component-wise

the thing is, I do not know how to apply that in such a complex function please help me.. teach me some sorcery

edit: btw, this limit is defined to be the derivative