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How do you get from ( |z| )^2 = a^2 + b^2 to -2z = -2a + 2i - b

Guest Sep 14, 2018
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How do you get from ( |z| )^2 = a^2 + b^2 to -2z = -2a + 2i *- b

You missed the times sign.

$$z=a+bi\\ \text{|z| is the distance of point Z from the origin.}\\ \text{Using pythagorases theorem we get }|z|^2=a^2+b^2\\ \\~\\ Since z=a+bi\\ -2z=-2(a+bi)\\ -2z=-2a-2bi$$

Melody  Sep 15, 2018