Determine where f'(z) exists and find its value when

$\displaystyle f(z)=x^2+iy^2$

My book gives NO explanation of how to find derivatives when the function f(z) isn't given in terms of z, as it is here. How do you solve these?

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- Jan 28th 2010, 01:06 PMpaupsersDerivative of Complex Function
Determine where f'(z) exists and find its value when

$\displaystyle f(z)=x^2+iy^2$

My book gives NO explanation of how to find derivatives when the function f(z) isn't given in terms of z, as it is here. How do you solve these? - Jan 28th 2010, 02:49 PMshawsend
Hi. But $\displaystyle x=\frac{z+\overline{z}}{2}$ and $\displaystyle y=\frac{z-\overline{z}}{2i}$ right? How about just using the chain rule then to compute $\displaystyle \frac{\partial f}{\partial z}$?

- Jan 28th 2010, 03:05 PMPlato
Here is the link you need.