## anonymous one year ago Find the magnitude of

1. anonymous
2. anonymous

j=i imaginary part

3. ganeshie8

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

4. ganeshie8

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

5. ganeshie8

simply take the square root

6. anonymous

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

7. anonymous

and how did the denominator turn to that form?

8. ganeshie8

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

9. ganeshie8

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

10. ganeshie8

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

11. anonymous

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

12. anonymous

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

13. ganeshie8

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

14. anonymous

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

15. ganeshie8

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

16. ganeshie8

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

17. anonymous

:)