1. ## Complex Number Equation

Hello. I would appreciate some help on this problem:

Find the solution of the equation:

$|z|-z=1-3i$

where z-complex number.

2. Originally Posted by javax
Hello. I would appreciate some help on this problem:

Find the solution of the equation:

$|z|-z=1-3i$

where z-complex number.
$z=a+ib$

$|z|=\sqrt{a^2+b^2}$

$|z|-z=\sqrt{a^2+b^2}-a-ib$

Solve by inspection for "b" and deduce "a".