# Math Help - complex plane

1. ## complex plane

Find the image of this region
{z : 1<=|z|<=2 and 0<= arg z <= pi/4}
under w(z)=1+1/z
z is complex number

Can anybody help me with this question please?

Thanks

2. Originally Posted by sidi
Find the image of this region
{z : 1<=|z|<=2 and 0<= arg z <= pi/4}
under w(z)=1+1/z
z is complex number
Here are some facts.
$w(z) = 1 + \frac{{\overline z }}
{{\left| z \right|^2 }}\;\& \,\arg \left( {\overline z } \right) = - \arg (z)$