- The locus of points \(z\) satisfies
$$| z + a \mathrm { i } | = 3 | z - a |$$
where \(a\) is an integer.
The locus is a circle with its centre in the third quadrant and radius \(\frac { 3 } { 2 } \sqrt { 2 }\)
Determine
- the value of \(a\),
- the coordinates of the centre of the circle.
\footnotetext{Question 5 continued
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