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

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To obtain the voltage gain |Vo/Vs| after finding Vo/Vs, one must calculate the magnitude of both the numerator and denominator, which are complex numbers. The magnitude can be determined using the Pythagorean theorem, considering the real and imaginary components of each complex number. The correct approach involves squaring both the real and imaginary parts, summing them, and then taking the square root. This method effectively provides the magnitude of the transfer function. Understanding these steps clarifies how to transition from Vo/Vs to |Vo/Vs|.
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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



b8650999aa.png


The correct answer given to us is below
bcbfdf8706.png


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.
 

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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 ...
 
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NascentOxygen said:
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!
 

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