The complex numbers u and v are given by u = 1 + 2sqrt3i and v = 3 + 2i. In an Argand diagram, u and v are represented by the points A and B. A third point C lies in the first quadrant and is
such that BC = 2AB and angle ABC = 90Å. Find the complex number z represented by C, giving
your answer in the form x + iy, where x and y are real and exact