The question:

Show that for any complex number z with |z| = 1.

My attempt:

I tried finding the the result of the division, hoping to get a value of 0 as the real part, to confirm the problem. This is what I got:

Let z = a+ib

Therefore the real part is:

Now I'm not sure where to go from here. I think what I've done so far is correct. Any help would be great, thanks!