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Math Help - Convert complex number to polar form?

  1. #1
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    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.
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  2. #2
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    Re: Convert complex number to polar form?

    Quote Originally Posted by stupidoldman View Post
    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 z is a complex number then \frac{1}{z}=\frac{\overline{z}}{~|z|^2}
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  3. #3
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    Re: Convert complex number to polar form?

    I don't see why inverting would not help, if z= re^{i\theta} then \frac{1}{z}= \frac{1}{r}e^{-i\theta}. 1+ jwcr has r= \sqrt{1+ w^2c^2r^2}, \theta= arctan(wcr).
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  4. #4
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    Re: Convert complex number to polar form?

    Hello, stupidoldman!

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

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

    Multiply numerator and denominator by the conjugate:

    . \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?

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