$|(1 + j2\pi fT)^2| = 1 + (2\pi fT)^2$

Question

I'm currently trying to understand why $|(1 + j2\pi fT)^2| = 1 + (2\pi fT)^2$ holds.

So far I have: $|(1 + j2\pi fT)^2| = |-4\pi^2 f^2T^2 + j4\pi fT + 1|$.

But why does $4\pi fT$ disappear? I know that $|j| = 1$.

Answer 1

For a complex number, $$|a+jb|=\sqrt{a^2+b^2}\ .$$ The easiest way in this case is $$|(1+j2\pi fT)^2|=|1+j2\pi fT|^2=1^2+(2\pi fT)^2\ .$$