Let z1 and z2 be two distinct points in the complex plane, and let K be a positive real constant that is greater than the distance between z1 and z2.
(a) Show that the set of points {z:∣z−z1∣+∣z−z2∣=K} is an ellipse with foci z1 and z2.
(b) Find the equation of the ellipse with foci ±3i that goes through the point 8−3i.
(c) Find the equation of the ellipse with foci ±2i that goes through the point 3+2i.