Yes, use the Cauchy-Riemann Equations. You don't need to convert back to Cartesians, the Cauchy-Riemann Equations in polar form are and .
Please refer to the attached image.
Could I get some hints on how to evaluate these question.
The question asking to find where is differentiable doesn't seem to involved,
however would I use C-R equations, or would it just be for wherever . Although that is given in the domain, so I'm assuming they want us to use C-R equations.
If i were to use C-R equations, then I would have to convert to cartesian coordinates, correct?
How would I do that.
As for the other question,
could I get any hints on what theorems may be relevant. I am not sure how to approach this.