1. ## Locus coordinates

The complex numbers w and z is represented by P (x , y) and Q (u, v) on argand diagrams and

$w=z^2$

P moves along the line $y=x-1$. Find the cartesian equation of the locus of Q.

I got expressions for u and v in terms of x and y first:

u = $x^2 - y^2$
v = $2xy$

Then I inserted the $y=x-1$ into the equations

u = $x^2 - x^2 + 2x - 1$
u = 2x - 1 --> $x = \frac{u+1}{2}$

v = 2xy
v = $2(\frac{u+1}{2})(\frac{u+1}{2} - 1)$

and my cartesian equation came out as

$v = u + 1$

Would it be possible if you could please verify my answer? Thanks if you can help

2. I'm not sure if I've substituted it correctly but all I'm looking for here is to confirm if it's right