Find the magnitude of

Question

anonymous · Answer

anonymous · Answer

j=i imaginary part

ganeshie8 · Answer

magnitudes get divided when you divide two complex numbers :
$$\left|\dfrac{z_1}{z_2}\right| = \dfrac{|z_1|}{|z_2|}$$

ganeshie8 · Answer

so the magnitude of $\large \eta^2 $ is given by :
$$\large |\eta^2| = \dfrac{\omega\mu}{\sqrt{\sigma^2+\omega^2\epsilon^2}}$$

ganeshie8 · Answer

simply take the square root

anonymous · Answer

Why did you take off the square root at the numerator only?

anonymous · Answer

and how did the denominator turn to that form?

ganeshie8 · Answer

the magnitude of numerator, $j\omega \mu$, is  just $|\omega \mu|$ right

ganeshie8 · Answer

its the same formula that you know

magnitude of $a+jb$ is given by $\sqrt{a^2+b^2}$

ganeshie8 · Answer

its just that mathematicians use $i$ and physicists use $j$

they both are same

anonymous · Answer

I need time to digest it. Thanks for explanation :)

anonymous · Answer

One more question: They ask for magnitude of $\eta$ , not $\eta^2$, why did you turn it to $\eta^2$?

ganeshie8 · Answer

$|\eta| = \sqrt{|\eta^2|}$

anonymous · Answer

And after going around, you get back to $|\eta|$, right? 
Thanks again. :)

ganeshie8 · Answer

Exactly, that wasn't supposed to be hard haha!

ganeshie8 · Answer

technically the answer is simply $ \sqrt{\dfrac{\omega\mu}{\sqrt{\sigma^2+\omega^2\epsilon^2}}}$

anonymous · Answer

:)