9709 P32 - Jun 2023 - Q5 - 6 marks
2005
Let \(a=2+yi\), where \(y\) is real and \(y<0\), and \(f(a)=a^3-a^2-2a\).
(a) Find a simplified expression for \(f(a)\) in terms of \(y\). [3]
(b) Given \(\operatorname{Re}f(a)=-20\), find \(\arg a\). [3]
