# Convert complex number to polar form?

• Nov 24th 2011, 12:58 PM
stupidoldman
Convert complex number to polar form?
Well, I need help converting 1/(1+j*w*c*r) to polar form, where j is the complex number sqrt(-1) and w,c,r are just variables. Can't split up the denominator to make it a sum of fractions, nor does inverting helps.

This equation is from a series connection with a voltage source to a resistor and capacitor, finding the voltage source of the capacitor (the Vin is not included in the equation I gave, or else it would be Vin/(1+j*w*c*r)).This question is here because I don't need help with the phasor analysis part, but rather the complex conversion part.
• Nov 24th 2011, 01:06 PM
Plato
Re: Convert complex number to polar form?
Quote:

Originally Posted by stupidoldman
Well, I need help converting 1/(1+j*w*c*r) to polar form, where j is the complex number sqrt(-1) and w,c,r are just variables. Can't split up the denominator to make it a sum of fractions, nor does inverting helps.

If $\displaystyle z$ is a complex number then $\displaystyle \frac{1}{z}=\frac{\overline{z}}{~|z|^2}$
• Nov 25th 2011, 05:49 AM
HallsofIvy
Re: Convert complex number to polar form?
I don't see why inverting would not help, if $\displaystyle z= re^{i\theta}$ then $\displaystyle \frac{1}{z}= \frac{1}{r}e^{-i\theta}$. 1+ jwcr has $\displaystyle r= \sqrt{1+ w^2c^2r^2}$, $\displaystyle \theta= arctan(wcr)$.
• Nov 25th 2011, 06:53 AM
Soroban
Re: Convert complex number to polar form?
Hello, stupidoldman!

Quote:

$\displaystyle \text{I need help converting }\frac{1}{1+wcr{\bf j}}\text{ to polar form,}$

. . $\displaystyle \text{where }{\bf j} = \sqrt{\text{-}1}\text{ and }w,c,r\text{ are constants.}$

Multiply numerator and denominator by the conjugate:

.$\displaystyle \frac{1}{1 + wcr{\bf j}} \cdot\frac{1- wcr{\bf j}}{1-wcr{\bf j}} \;=\;\frac{1-wcr{\bf j}}{1 + w^2c^2r^2} \;=\;\frac{1}{1+w^2c^2r^2} - \frac{2wcr}{1+w^2c^2r^2}{\bf j}$

Got it?