$$z _ { 1 } = a + b \mathrm { i } \text { and } z _ { 2 } = c + d \mathrm { i }$$
where \(a , b , c\) and \(d\) are real constants.
Given that
\(b > d\)
\(z _ { 1 } + z _ { 2 }\) is real
\(\left| z _ { 1 } \right| = \sqrt { 13 }\)
\(\left| z _ { 2 } \right| = 5\)
\(\operatorname { Re } \left( z _ { 2 } - z _ { 1 } \right) = 2\)
show that \(a = 2\) and determine the value of each of \(b , c\) and \(d\)
(a) On the same Argand diagram
sketch the locus of points \(z\) which satisfy \(| z - 12 | = 7\)
sketch the locus of points \(w\) which satisfy \(| w - 5 \mathrm { i } | = 4\) showing the coordinates of any points of intersection with the axes.
(b) Determine the range of possible values of \(| z - w |\) [0pt]
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