Hey I've got two questions (no answers so ones more of just double checking some working!)

Firstly can someone have a look over this for me:

my reasoning is this

$\displaystyle z-c=\rho (\frac{(1+it)^2}{(1-it)(1+it)})$

$\displaystyle z-c=\rho (\frac{1-t^2}{1+t^2}+\frac{2t}{1+t^2}i)$

if we change the parameter now by letting $\displaystyle t=\tan \frac{\theta}{2}$

we then have

$\displaystyle z-c=\rho (cos \theta + i\sin \theta)$

so this would be a circle of radius $\displaystyle \rho$ centered on c

as $\displaystyle |z-c|=|\rho|$

(does this get around the problem that $\displaystyle \rho$ can be negative?)

or did I screw up somewhere!

and for the second question any chance of a little hint because I cant see where to start with this

for this ive worked out that the final condition implys that if each of the numbers a,b,c were written as $\displaystyle x_a+y_at$ etc.

then $\displaystyle x_cy_b=x_by_c$ but I cant see a way to apply it so any chance of a hint

many thanks

Simon