A simple Complex Analysis Mapping

[NewtonianAlch]

Homework Statement

http://img684.imageshack.us/img684/779/334sn.jpg

The Attempt at a Solution

The first part was fairly straightforward, solve for z + 1, and then get w in terms of u + iv, rationalise the denominator, and then we get (x,y) in terms of u and v, which we substitute back into the equation of the line, and get it into the form of an equation of a circle.

The next part is not as obvious for me, I tried the same method, but I couldn't rationalise the denominator, I'm assuming the circle is shifted somehow because of the 2, but I'm not sure.

 

[dimension10]

Homework Statement

http://img684.imageshack.us/img684/779/334sn.jpg

The Attempt at a Solution

The first part was fairly straightforward, solve for z + 1, and then get w in terms of u + iv, rationalise the denominator, and then we get (x,y) in terms of u and v, which we substitute back into the equation of the line, and get it into the form of an equation of a circle.

The next part is not as obvious for me, I tried the same method, but I couldn't rationalise the denominator, I'm assuming the circle is shifted somehow because of the 2, but I'm not sure.

If you can't do it with complex numbers, switch to vectors.