a) The functions, f, g and h are defined by f(x) = x2 + a, g(x) = 3x + 2 and h(x) = 9x2 + 12x + 11 respectively. (i) If h(x) = f g(x), find the value of the constant a.

(ii) Determine the inverse function of f for x > 0.

(b) The point A has coordinates A(-5, 1) and the point B has coordinates B(3, q). The point M is the midpoint of the line segment AB and has coordinates M(p, -7). (i) Determine the values of the constants p and q.

(ii) Determine the equation of the straight line which is perpendicular to the line segment AB and which passes through the point M. Give your answer in the form ax + by + c = 0, where a, b and c are integers.

The cubic polynomial f(x) = x3 + ax + b has a factor of x ? 1 and a remainder of 6 when divided by x + 1. Find the values of the constants a and b.

(d) Three complex numbers, w. y and z; are represented on an Argand diagram below.