Finding the Angle of a Complex Number: Tips and Tricks

[asi123]

Homework Statement

Hey guys.
I have the next transfer function

http://img195.imageshack.us/img195/7924/scan0002l.jpg

And I want to find the angle of it.
I know I can break it into REAL and IMAGINARY but I'm looking for a faster way, is there?

Thanks.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

I have the next transfer function

And I want to find the angle of it.

Hi asi123!

Hint: if w R and C are all real, then the angle (phase) of 1 + jwRC is arctan(wRC)

 

[gabbagabbahey]

I know I can break it into REAL and IMAGINARY but I'm looking for a faster way, is there?

Not really; finding the real and imaginary parts here is fairly quick. Just multiply both the numerator and denominator by the conjugate of the denominator, then $$\phi=\arctan\left(\frac{\text{Im}[H]}{\text{Re}[H]}\right)$$.

 

[asi123]

Not really; finding the real and imaginary parts here is fairly quick. Just multiply both the numerator and denominator by the conjugate of the denominator, then $$\phi=\arctan\left(\frac{\text{Im}[H]}{\text{Re}[H]}\right)$$.

For this on, but I'm asking in general.

Thanks.

 

[asi123]

Hi asi123!

Hint: if w R and C are all real, then the angle (phase) of 1 + jwRC is arctan(wRC)

Ok, I don't see any logic in that.
This is not a homework question, I know the answer, why would you give me a hint?
Is there a rule how to get to the angle?

Thanks.