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

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 $$|j| = 1$$.

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