I'm not sure where to start with this question at all, some help would be appreciated

A point Z in an Argand diagram represents $\displaystyle z = e^i \theta$

By writing z + 1 as $\displaystyle e^(1/2i\theta) (e^(1/2i\theta) + e^(-1/2i\theta)$, find the modulus and argument of z+1.

Hmm, the editing has gone badly, it should be:

e^(itheta) in the first and

e^(0.5itheta)(e^(0.5itheta) + e^(-0.5itheta)) in the second.