a) Let z = x + iy where x = Re z, y = Im z and so x and y R). Express the perpendicular distance from z to the real axis in terms of x and/or y. (Hint: draw a diagram.) (b) Consider a parabola, drawn on a plane. The perpendicular distance of each point on the parabola from a given line (the directrix) is equal to its distance from a given point (the focus). Sketch the set P = {z C | |Im z| = |z i|} in the complex plane. Indicate the directrix and focus of the resulting parabola and show the point where the parabola intersects the imaginary axis. (c) By setting z = x + iy where x and y R, derive an equation for the parabola in the previous part in terms of the real and imaginary parts of z.