Why |1+6 omega i−9 omega^2|=1+9 omega^2 2,omega>0 Where does the 6 omega go?

veXslefsskink09

veXslefsskink09

Open question

2022-08-24

Why:
| 1 + 6 ω i 9 ω 2 | = 1 + 9 ω 2 , ω > 0

Answer & Explanation

Mario Kerr

Mario Kerr

Beginner2022-08-25Added 5 answers

It’s just the Pythagorean theorem applied to the real and imaginary parts of the number:
| 1 + 6 ω i 9 ω 2 | = ( 1 9 ω 2 ) 2 + ( 6 ω ) 2 = 1 18 ω 2 + 81 ω 4 + 36 ω 2 = 1 + 18 ω 2 + 81 ω 4 ,
and from here you should have no trouble finishing.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?