9709 P33 - Jun 2022 - Q5 - 8 marks
1927
The complex number \(3-i\) is denoted by \(u\).
(a) Show, on an Argand diagram with origin O, the points A, B and C representing the complex numbers \(u\), \(u^*\) and \(u^*-u\) respectively. State the type of quadrilateral formed by the points O, A, B and C. [3]
(b) Express \(u^*/u\) in the form \(x+iy\), where \(x\) and \(y\) are real. [3]
(c) By considering the argument of \(u^*/u\), or otherwise, prove that \(\tan^{-1}(3/4)=2\tan^{-1}(1/3)\). [2]
