4 Two complex numbers, \(\alpha\) and \(\beta\), are given by \(\alpha = 1 - 2 \mathrm { j }\) and \(\beta = - 2 - \mathrm { j }\).
- Represent \(\beta\) and its complex conjugate \(\beta ^ { * }\) on an Argand diagram.
- Express \(\alpha \beta\) in the form \(a + b \mathrm { j }\).
- Express \(\frac { \alpha + \beta } { \beta }\) in the form \(a + b \mathrm { j }\).