SOLUTION: Find all complex numbers z such that |z|^2-2(con-z)+iz=2i, where the absolute value sign represents the distance of the complex number from the origin of a complex plane and (con-

Question 1021503: Find all complex numbers z such that
|z|^2-2(con-z)+iz=2i, where the absolute value sign represents the distance of the complex number from the origin of a complex plane and (con-z) represents the complex conjugate of z.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let z = x+iy
==>
=
Since this is supposed to be equal to 2i, it follows that
x+2y = 2 and
Putting x = 2-2y into , we get

Simplifying this and solving for y (you should be able to do the algebra!), we get
y = 0 or y=1.
The corresponding x-values are x = 2 or x = 0 respectively..
Therefore there are two complex numbers satisfying the original equation namely
, and .
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