How do you get from ( |z| )^2 = a^2 + b^2 to -2z = -2a + 2i *- b
You missed the times sign.
\(z=a+bi\\ \text{|z| is the distance of point Z from the origin.}\\ \text{Using pythagorases theorem we get }|z|^2=a^2+b^2\\ \\~\\ Since z=a+bi\\ -2z=-2(a+bi)\\ -2z=-2a-2bi\)
