XPD127 Mathematics 1A 1. (a) The complex number z = 1 - 2 is a root of the polynomial p( z) = 23 + mz - b. where b and m are real numbers. Determine the linear factors of p(z) and the [6 marks] values of b and m. (b) Let z = -3V3+3i. Determine z, |z |, z and In(z). [5 marks] (c) Show that (1 + i)n - (1 - 2)2 = 22+1. isin (") ) for all n E Z. [4 marks]