9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{78543314-72b7-4366-98a1-dbb6b852632f-30_312_634_278_717}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a locus in the complex plane.
The locus is an arc of a circle from the point represented by \(z _ { 1 } = 3 + 2 i\) to the point represented by \(z _ { 2 } = a + 4 \mathrm { i }\), where \(a\) is a constant, \(a \neq 1\)
Given that
- the point \(z _ { 3 } = 1 + 4 \mathrm { i }\) also lies on the locus
- the centre of the circle has real part equal to - 1
- determine the value of \(a\).
- Hence determine a complex equation for the locus, giving any angles in the equation as positive values.