# Math Help - Complex Analysis: Parallelogram Law

1. ## Complex Analysis: Parallelogram Law

I need to prove the parallelogram law for complex numbers z and w: $|z+w|^2+|z-w|^22|z|^2+2|w|^2$. My approach follows:
Proof: $|z+w|^2+|z-w|^2=|z|^2+2|wz|+|w|^2+|z|^2-2|wz|+|w|^2=2|z|^2+2|w|^2$

Can I actually multiply |z+w| in this format? Thanks.

2. ## Re: Complex Analysis: Parallelogram Law

You can't do it like that because you're dealing with absolute value bars and not parentheses. Instead, start with
$|z+w|^2=(z+w)(\overline{z+w})$

3. ## Re: Complex Analysis: Parallelogram Law

Thanks so much! I knew I had missed a property somewhere!