5.
$$z = 5 + \mathrm { i } \sqrt { 3 } , \quad w = \sqrt { 3 } - \mathrm { i }$$
- Find the value of \(| w |\).
Find in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are real constants,
- \(z w\), showing clearly how you obtained your answer,
- \(\frac { z } { w }\), showing clearly how you obtained your answer.
Given that
$$\arg ( z + \lambda ) = \frac { \pi } { 3 } , \quad \text { where } \lambda \text { is a real constant, }$$
- find the value of \(\lambda\).