1.
$$z = 3 + 2 \mathrm { i } , \quad w = 1 - \mathrm { i }$$
Find in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are real constants,
- \(z w\)
- \(\frac { z } { w ^ { * } }\), showing clearly how you obtained your answer.
Given that
$$| z + k | = \sqrt { 53 } \text {, where } k \text { is a real constant }$$
- find the possible values of \(k\).