Complex number

Posted March 17th, 2011 by alpha

If z is a complex number satisfying the relation $|z+1|=z+2(1+i)$ , then find z.

Seeking an urgent reply.

Comments

On March 18th, 2011 Structure says:

im z+2+2i=0
So if z=x+iy you must have y=-2
so $|x+1+2i|=x+2$

$$x^2+2x+1+4=x^2+4x +4$

$x=\frac{1}{2}$

$z=\frac{1}{2}-2i$