8 Two loci, \(C _ { 1 }\) and \(C _ { 2 }\), are defined by
$$\begin{aligned}
& C _ { 1 } = \left\{ z : | z | = \left| z - 4 d ^ { 2 } - 36 \right| \right\}
& C _ { 2 } = \left\{ z : \arg ( z - 12 d - 3 i ) = \frac { 1 } { 4 } \pi \right\}
\end{aligned}$$
where \(d\) is a real number.
- Find, in terms of \(d\), the complex number which is represented on an Argand diagram by the point of intersection of \(C _ { 1 }\) and \(C _ { 2 }\).
[0pt]
[You may assume that \(C _ { 1 } \cap C _ { 2 } \neq \varnothing\).] - Explain why the solution found in part (a) is not valid when \(d = 3\).
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\section*{OCR
Oxford Cambridge and RSA}