9. Given that
$$\frac { z - k \mathrm { i } } { z + 3 \mathrm { i } } = \mathrm { i } \text {, where } k \text { is a positive real constant }$$
- show that \(z = - \frac { ( k + 3 ) } { 2 } + \frac { ( k - 3 ) } { 2 } \mathrm { i }\)
- Using the printed answer in part (a),
- find an exact simplified value for the modulus of \(z\) when \(k = 4\)
- find the argument of \(z\) when \(k = 1\). Give your answer in radians to 3 decimal places, where \(- \pi < \arg z < \pi\)