- The locus of points \(z = x + \mathrm { i } y\) that satisfy
$$\arg \left( \frac { z - 8 - 5 i } { z - 2 - 5 i } \right) = \frac { \pi } { 3 }$$
is an arc of a circle \(C\).
- On an Argand diagram sketch the locus of \(z\).
- Explain why the centre of \(C\) has \(x\) coordinate 5
- Determine the radius of \(C\).
- Determine the \(y\) coordinate of the centre of \(C\).