SPS SPS FM Pure 2023 June — Question 10

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2023
SessionJune
TopicComplex Numbers Arithmetic
TypeComplex number parameter problems
10. The complex number \(z\) is given by \(z = k + 3 i\), where \(k\) is a negative real number. Given that \(z + \frac { 12 } { z }\) is real, find \(k\) and express \(z\) in exact modulus-argument form.
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