9 Two complex numbers, \(\alpha\) and \(\beta\), are given by \(\alpha = 1 + \mathrm { j }\) and \(\beta = 2 - \mathrm { j }\).
- Express \(\alpha + \beta , \alpha \alpha ^ { * }\) and \(\frac { \alpha + \beta } { \alpha }\) in the form \(a + b \mathrm { j }\).
- Find a quadratic equation with roots \(\alpha\) and \(\alpha ^ { * }\).
- \(\alpha\) and \(\beta\) are roots of a quartic equation with real coefficients. Write down the two other roots and find this quartic equation in the form \(z ^ { 4 } + A z ^ { 3 } + B z ^ { 2 } + C z + D = 0\).