I. Consider the polynomial equation 2:3 8 = 0. Solve this equation using two different methods and show that both methods produce the same set of solutions. (Useful fact: a3 b3 = (a lb)(o.2 + 013+ (32).) L. (a) (b) Let 2 = :1: + iy where :1: = Rez, y = 11112 and so :1: and y E R). Express the perpendicular distance from z to the real axis in terms of 3: and /or y. (Hint: draw a diagram.) 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 E (C | |Imz| = Iz - ill} in the complex plane. Indicate the directrix and focus of the resulting parabola and Show the point where the parabola intersects the imaginary axis. By setting z = a: + iy where :1: and y e R, derive an equation for the parabola in the previous part in terms of the real and imaginary parts of z