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

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

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