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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 $|j| = 1$.

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

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  • $\begingroup$ Thanks, very simple indeed. $\endgroup$ – Zelda_CompSci Feb 17 at 23:55

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