l. Consider the polynomial equation 23 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 Il1a)(n2 + ab + 52).) L. (a) (1)) Let 2 = :1: + iy where :1: = Rez, y = Imz 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 = {2: E (C | |Imz| = Iz - il} 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 = :1: + 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