9709 P33 - Jun 2018 - Q9
1960
(a) Find the complex number z satisfying the equation
\(3z - iz^* = 1 + 5i\),
where \(z^*\) denotes the complex conjugate of \(z\).
(b) On a sketch of an Argand diagram, shade the region whose points represent complex numbers \(z\) which satisfy both the inequalities \(|z| \leq 3\) and \(\text{Im } z \geq 2\), where \(\text{Im } z\) denotes the imaginary part of \(z\). Calculate the greatest value of \(\arg z\) for points in this region. Give your answer in radians correct to 2 decimal places.
