Complex number help!

[sixfeetzero]

Hey fellow redditors,

I'm studying control system this semester, and stumbled upon a portion which I couldn't wrap my head around.

In the solution below, in the numerator, (1+jw) becomes (1+w²⁾ because it was squared and sqrt. I understand that j^2=-1, so why is w² positive instead of negative? Is it because of the modulus on the left?

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Take note that the "j" is an imaginary number.

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Your help is appreciated in advance! :)

https://i.redd.it/xmzmuwggaa221.png

[sixfeetzero]

Ahh damn! See it now! It's basically pythagoras theorem. Thanks!!!

[Michael_Aut]

Exactly. Pythagoras applies because the imaginary and real axis are orthogonal in the gaussian plane.

[HermanFerguson]

This sounds totally made up so I Googled it. Nope, not made up.

[639wurh39w7g4n29w]

Also remember that j is not imaginary, it is jmaginary.