4.
$$z _ { 1 } = 3 \mathrm { i } \text { and } z _ { 2 } = \frac { 6 } { 1 + \mathrm { i } \sqrt { 3 } }$$
- Express \(z _ { 2 }\) in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are real numbers.
- Find the modulus and the argument of \(z _ { 2 }\), giving the argument in radians in terms of \(\pi\).
- Show the three points representing \(z _ { 1 } , z _ { 2 }\) and \(\left( z _ { 1 } + z _ { 2 } \right)\) respectively, on a single Argand diagram.