11.Given that = 2 i, z , find z in the form a + ib.(Total 4 marks)

2.A geometric sequence u1, u2, u3, ... has u1 = 27 and a sum to infinity of .(a)Find the common ratio of the geometric sequence.(2) An arithmetic sequence v1, v2, v3, ... is such that v2 = u2 and v4 = u4.(b)Find the greatest value of N such that .(5)(Total 7 marks)

3.The diagram below shows a circle with centre O. The points A, B, C lie on the circumference of the circle and [AC] is a diameter.Let . (a)Write down expressions for in terms of the vectors a and b.(2) (b)Hence prove that angle is a right angle.(3)(Total 5 marks)

4.(a)Show that = tan .(2) (b)Hence find the value of cot in the form a + , where a, b .(3)(Total 5 marks)