# Question: the locus of a set of points z is a...

###### Question details

The locus of a set of points *z* is a circle with centre 0 + *i* and radius 2. Given that $w=\frac{z-2}{z-i}z\ne i$ prove that the locus of all such points *w *is another circle. Determine the centre and the radius of this new circle. [4 marks]

Please show all working (even the simple steps).