Show a complex function is differentiable at 0

(Sorry for all the questions on this, I am really struggling with this and really appreciate all help.)

Show that the function is differentiable at the origin.

So if , then .

To show that it's differentiable you have to show that the limit of the difference quotient exists at 0:







Is this the right way to start?

Hey Ragnarok.

Hint: You might want to try looking at the Cauchy-Riemann equations. Have you come across these in class?

Ah, we have covered the Cauchy-Riemann equations, though technically this problem is from a section before they are covered. I think it will work fine, though, thanks for the hint!