Hi, I've been asked to show the following for a complex number z

Attempt:

If I let z = a +bi and do the algebra I end up with

a^{2}- b^{2}+2abi / a^{2 }+ b^{2 }= 1

And I can't see how this could always be true?

If I follow this through I get ai = b ?

Help would be greatly appreciated this is driving me nuts! thanks in advance :-)