How to get rid of the absolute value when solving a system of complex equations?

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