I'm trying to solve a system of complex equations, but I don't know how to deal with the absolute value (magnitude of the complex number). I had the idea of squaring both sides to make it go away, but I wasn't sure if this is valid (aside from making it more complicated). What's the right way to approach solving equations with absolute value in them such as the following system

$$ \frac{G}{|(0.1253-i0.9921)r^2-(1.3602-i0.8044)r+1|} = \frac{1}{2} $$

and the second equation is $$ \frac{G}{|(0.3681-i0.9298)r^2-(1.3681-i0.9298)r+1|} = 1 $$

  • $\begingroup$ Squaring is fine. It doesn't make the modulus "go away", but rather $|z|^2 = z\overline{z}.$ $\endgroup$ – B. Goddard Apr 27 '18 at 14:06
  • $\begingroup$ Is there another way? By-hand calculations become more complicated. $\endgroup$ – YoZo Apr 27 '18 at 14:10
  • $\begingroup$ Also, if I were to use MATLAB to solve them, do I just use the abs() function in MATLAB? $\endgroup$ – YoZo Apr 27 '18 at 14:11

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