Question: The Complex number $z$ is represented by the point $T$ in the Argand Diagram.Given that $$z =\frac{1}{3+it}$$ where $t$ is a variable, show that
i) as $t$ varies, $T$ lies on a circle, and state the coordinates of the centre of this circle.
The only thing I did was put $z =\frac{1}{3+it}$ into the form $z =\frac{3}{9+t^2}-\frac{t}{9+t^2}i$ by multipliying $z$ by it's conjugate, but I dont know where to go from there.Help anyone?