23 i47 1. Consider the complex number z = . (1 + i)3 (a) Show that z can be expressed in the Cartesian form 2 2i. (b) Write z in polar form using the principal argument. z6 in polar form using the principal argument. z5 (a) Find the sixth complex roots of 12 (1 3i). (c) Write 2. (b) Plot and label the roots in the complex plane. (c) Let A = {z C|z 6 = 12 (1 3i)} and B = {z C|Im(z) > 12 }. Determine A \\ B, and express it in set notation . 3. Let p(z) = z 4 9z 3 + 29z 2 55z + 50. Find all roots of the polynomial equation p(z) = 0, where z C, given that 1 2i is one root. 2