7.
$$z = - 3 k - 2 k \mathrm { i } , \text { where } k \text { is a real, positive constant. }$$
- Find the modulus and the argument of \(z\), giving the argument in radians to 2 decimal places and giving the modulus as an exact answer in terms of \(k\).
- Express in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are real and are given in terms of \(k\) where necessary,
- \(\frac { 4 } { z + 3 k }\)
- \(z ^ { 2 }\)
- Given that \(k = 1\), plot the points \(A , B , C\) and \(D\) representing \(z , z ^ { * } , \frac { 4 } { z + 3 k }\) and \(z ^ { 2 }\) respectively on a single Argand diagram.