Difficult complex numbers

The complex numbers Z and W are represented, respectively, by points P(x, y) and Q(u,v) in Argand diagrams and

W=1/(Z+1)

By first writing Z+1=1/W

(a) Show that

x+1=u/(u²+v²)

and find an expression for y in terms of u and v.

(b) The point P moves along the circle (x+1)² + y² = 4. Find the equation of the locus Q.

Could somebody please show a step by step solution to this please? I really don't know how to answer these type of questions. Is there a general method?

Thanks

Dan