9709 P32 - Nov 2022 - Q5 - 8 marks
1924
(a) Solve the equation \(z^2-6iz-12=0\), giving the answers in the form \(x+iy\), where \(x\) and \(y\) are real and exact. [3]
(b) On a sketch of an Argand diagram with origin O, show points A and B representing the roots of the equation in part (a). [1]
(c) Find the exact modulus and argument of each root. [3]
(d) Hence show that the triangle OAB is equilateral. [1]
