13. Given that \(z = 3 - 3 i\) express, in the form \(a + i b\), where \(a\) and \(b\) are real numbers,
- \(z ^ { 2 }\),
(2) - \(\frac { 1 } { z }\).
(2) - Find the exact value of each of \(| z | , \left| z ^ { 2 } \right|\) and \(\left| \frac { 1 } { z } \right|\).
(2)
The complex numbers \(z , z ^ { 2 }\) and \(\frac { 1 } { z }\) are represented by the points \(A , B\) and \(C\) respectively on an Argand diagram. The real number 1 is represented by the point \(D\), and \(O\) is the origin. - Show the points \(A , B , C\) and \(D\) on an Argand diagram.
- Prove that \(\triangle O A B\) is similar to \(\triangle O C D\).