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

$\displaystyle w=z^2$

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

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

u = $\displaystyle x^2 - y^2$

v = $\displaystyle 2xy$

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

u = $\displaystyle x^2 - x^2 + 2x - 1$

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

v = 2xy

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

and my cartesian equation came out as

$\displaystyle v = u + 1$

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