Why do you do that? Is it simply because that's the method to work out the real and imaginary parts when you are in a situation like this?
If z=a+bi then zˉ=a−bi, and so zzˉ=a2+b2=∣z∣2.
But then, z1=z1×zˉzˉ=∣z∣2zˉ.
This is the rule they've used. That is, that a+bi1=a2+b2a−bi. This then allows you to separate the real and imaginary part. You wouldn't get any marks for the answer you gave, because it's not right.