The complex number 3 − i is denoted by u. Its complex conjugate is denoted by u*.
i. On an Argand diagram with origin O, show the points A, B and C representing the complex numbers u, u* and u* − u respectively. What type of quadrilateral is OABC?

ii. Showing your working and without using a calculator, express u*/u in the form x + iy, where x and y are real.

iii. By considering the argument of u*/u, prove that

Transcribed Image Text:

¹(²)= 4 -1 tan 2 tan (3).