Let

(a) express z in modulus-argument form

(b) express z in real-imaginary form

First Question: Do I need to expand out the top and bottom parts before doing anything else?

Edit: This is what I got for (b):

expanding the denominator out, we get (-2 + 2i)

multiplying by gives =

expanding out gives:

thus:

hence:

correct? yes/no?

Any help for part (a) greatly appreciated!

FURTHER EDIT:

I've been through Moo's workings, adding in the cube power he missed and got the following:

(using Moo's notation of x, y, & t)

which gives:

which is ever-so-slightly different to what I got by expanding it all out.

What the hell am I doing wrong here?! I've spent 1/2 the morning going over this and just can't for the life of me see where I've gone wrong. Any help desperately appreciated!