9. Given that \(z _ { 1 } = 3 + 2 i\) and \(z _ { 2 } = \frac { 12 - 5 i } { z _ { 1 } }\),
- find \(z _ { 2 }\) in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are real.
- Show on an Argand diagram the point \(P\) representing \(z _ { 1 }\) and the point \(Q\) representing \(z _ { 2 }\).
- Given that \(O\) is the origin, show that \(\angle P O Q = \frac { \pi } { 2 }\).
The circle passing through the points \(O , P\) and \(Q\) has centre \(C\). Find
- the complex number represented by C,
- the exact value of the radius of the circle.