How to get |Vo/Vs| after finding Vo/Vs

[CoolDude420]

Homework Statement

This is probably a stupid question, but I'm not too sure how to obtain the "Voltage gain |Vo/Vs| after finding Vo/Vs which I think is called the transfer function".

I'm doing a question where I found the Vo/Vs but I'm not sure how to turn that into |Vo/Vs|

Homework Equations

The Attempt at a Solution

The correct answer given to us is below

The answer seems to have squared top and bottom and taken the square root of the bottom? Not entirely sure what's the general method for this.

 

[NascentOxygen]

Consider first the denominator. It is a complex number, and has a Real component and an Imaginary component. You can sketch it. To find the magnitude of a complex number, use Pythagoras.

The numerator is also a complex number ...

 

[CoolDude420]

Consider first the denominator. It is a complex number, and has a Real component and an Imaginary component. You can sketch it. To find the magnitude of a complex number, use Pythagoras.

The numerator is also a complex number ...

Ah. Got it! Took the magnitude of the top and the bottom. Thank you!