) Find all the complex numbers that satisfy z3 = 4v2(1+ i). Write your answers inthe exponential form.[3 marks] \text { (b) Calculate }(1+\sqrt{3} i)^{8} \text {. Write your answers

in the exponential form. } (c) If w = u + iv, z = x + iy and w = eiz, find u and v in terms of x and y. (d) The figures in the following table give the average weight (in kg) of an aircraft component for the years 2000, 2001, 2002 and 2003. Estimate the weight of the aircraft component in 2005.