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I was looking at a problem in a textbook and found the following simplification:

$$\frac{1}{x+i\omega} * \frac{2y}{y^2 + \omega^2} = \frac{2}{xy} * \frac{1}{1+i\frac{\omega}{x}}*\frac{1}{1 + (\frac{\omega}{y})^2}$$

and I have no clue how they did this simplification? Is this like some well known formula? I tried multiplying by the complex conjugate but that doesn't seem to help so any guidance/formulas they used would be much appreciated.

Thanks

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    $\begingroup$ Divide top and bottom by $y^2$, and $x+i\omega=x\left(1+i\frac\omega x\right)$ $\endgroup$
    – J. W. Tanner
    Nov 24, 2020 at 2:23
  • $\begingroup$ got it thank you! $\endgroup$
    – Evan
    Nov 24, 2020 at 2:29

1 Answer 1

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Divide top and bottom by $y^2$, and $x+i\omega=x\left(1+i\frac\omega x\right)$

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