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