Complex Numbers - Find the proof for "z"

Hi I have a question on complex numbers, where I'm not sure how to go about dealing with it.

This is what I need to do:

Let $z=a+ib$, be a complex number. Show that a square root of $z$, is given by the expression:
$$w=\sqrt{(\mid z\mid +a)/2} + i\sigma\sqrt{(\mid z\mid -a)/2}$$
where $\sigma=1$ if $b≥0$ and $\sigma=-1$ if $b<0$. Do this by verifying that $w^2=z$.

Do i need to go about this by starting with $w=\sqrt z=\sqrt{a+ib}$ and then manipulating the $a+ib$ part, or how would I do this?

Thanks.