# application of complex variables

#### tigertym

Joined Aug 18, 2007
3
"Your next step is to realize that if anything in the expression depends on frequency, then you can plot graphs of magnitude and phase as functions of frequency.
Try this for F(jw) = 1/(1+jwRC)"

I'm not sure exactly how to do this and am looking for any help. I understand that I need to multiply by the conjugate, but I'm not sure that I am doing it correctly. My answer is : 1+ωRCj/2

Additionally, I'm not sure exactly how to derive and plot magnitude and phase. I don't believe that plotting will be difficult, my uncertainty lies in calculating the magnitude and phase.

Any and all help is welcome.
Thanks!

#### hgmjr

Joined Jan 28, 2005
9,029
One posting of your question is sufficient. Since it is homework, you placed it in the most appropriate location.

I am going to delete the duplicate posting in the Math forum to prevent confusion later.

You may gain greater insight into the manipulation of complex numbers by reviewing the AAC tutorial on complex number arithmetic.

hgmjr

#### tigertym

Joined Aug 18, 2007
3

#### mcm200

Joined Apr 16, 2006
2
You can calculate the magnitude of the response of the circuit by taking into account that it is equal to the magnitud of the numerator divided by the magnitud of the denominator. In this case the magnitud of the numerator is 1 (real number) and the magnitud of the denominator is that of a complex number, that is, the square root of the sum of the squares of its real component and its imaginary component. In this case also, the denominator is raised to the nth power, so you have to raise the magnitud of the denominator to the same power. As for the phase, it is equal to the phase of the numerator minus the phase of the denominator, the phase of the numerator is zero (real number) and that of the denominator is the arctg of the quotient between the imaginary part and the real part. If, as in this case, the denominator is raise to a a power, you must multiply the resultant angle by this power.
Greetings and hope to have helped you.
Mako