Hi! I'm not quite sure if this belongs in this subforum due to the complex variable, but I couldn't find any other logical place to ask this question.

Here's the problem I have troubles solving:

Given f(z)=|z|sin(z) , determine f'(z), where it exists, and state where f is analytic and where it is not.

Of course, z is a complex variable such as z=x+iy.

I've first tried with the Cauchy Riemann equations, but I end up with something quite messy that is unsolvable from what I see.

How should I proceed?

Thanks.