Question 4 (a) Find a in the form of x + ty, if = = = + . provided that b = -2 + 4i and c = 2 + i. (6 marks) (b) Given the complex numbers, u = 4 - 2i and v = 3 + i. Express w = #*+1 # in the form x + yi, where x and y are real numbers. (5 marks) (c) Consider the complex number z = a + bi, where the modulus of z is 6 and the argument of z is - , find (i) the values of a and b (2 marks) (ii) the value of |z2| (3 marks) (d) Given that z1 = 5 + 2i and z2 = 2 - 3i, express = in polar (trigonometric) form. (5 marks) 30 (e) Use De Moivre's theorem to express (- - in the form a + bi, where a and b are real numbers. (4 marks) [Total : 25 marks] END OF QUESTION PAPER