9 The complex number \(z\) is such that
$$z = \frac { 1 + \mathrm { i } } { 1 - k \mathrm { i } }$$
where \(k\) is a real number.
9
- Find the real part of \(z\) and the imaginary part of \(z\), giving your answers in terms of \(k\)
9 - In the case where \(k = \sqrt { 3 }\), use part (a) to show that
$$\cos \frac { 7 \pi } { 12 } = \frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$$
\(\_\_\_\_\) The region \(R\) on an Argand diagram satisfies both \(| z + 2 \mathrm { i } | \leq 3\) and \(- \frac { \pi } { 6 } \leq \arg ( z ) \leq \frac { \pi } { 2 }\)