
Locus coordinates
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 $\displaystyle y=x1$. 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 $\displaystyle y=x1$ 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 :)

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