I need this one result to do a problem correctly.
I want to show that for any $b \in \mathbb{C}$ and $z$ a complex variable:
$ |z^2 + b^2| \geq |z|^{2} - |b|^{2}$
My attempts have only led me to conclude that
$ |z^2 + b^2| > \frac{|z|^{2} + |b|^{2}}{2}$