Complex function

Exercise2.1

1. For $w = z^2$, express $x,y$ using $u,v$ function and find out what curve is mapped to the $w$ plane parallel to the real and imaginary axes of the $z$ plane.

2. Express $u,v$ as a function of $x,y$ for the following function

(a)

$w = z^3$

(b)

$w = \frac{z}{z+1}$

(c)

$w = \frac{z - i}{z + i}$