- #1

gtfitzpatrick

- 380

- 0

## Homework Statement

Prove from first principles that f(z) = [itex]\overline{z}^2[/itex] is not differentiable at any point z ≠ 0

## Homework Equations

## The Attempt at a Solution

So i guess i Have to show [itex]\stackrel{lim}{h\rightarrow0} \frac{f(z+h)-f(z)}{h}[/itex] is equal to zero right?

[itex] \frac{\overline{z+h}^2-\overline{z}^2}{h}[/itex] but not sure where to go from here.

Do i use z=(x+iy) then [itex]\overline{z} = x-iy [/itex] and so [itex]\overline{z}^2[/itex] = [itex]x^2-y^2-i2xy [/itex]