- Given that
$$\begin{aligned}
z _ { 1 } & = 2 + 3
\left| z _ { 1 } z _ { 2 } \right| & = 39 \sqrt { 2 }
\arg \left( z _ { 1 } z _ { 2 } \right) & = \frac { \pi } { 4 }
\end{aligned}$$
where \(z _ { 1 }\) and \(z _ { 2 }\) are complex numbers,
- write \(z _ { 1 }\) in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\)
Give the exact value of \(r\) and give the value of \(\theta\) in radians to 4 significant figures.
- Find \(z _ { 2 }\) giving your answer in the form \(a + \mathrm { i } b\) where \(a\) and \(b\) are integers.