Chapter 2.16, Problem 1P

Show that if the line through the origin and the point z is rotated 90⁰ about the origin, it becomes the line through the origin and the point iz. This fact is sometimes expressed by saying that multiplying a complex number by i rotates it through 90⁰. Use this idea in the following problem. Let $z=a^{i\omega t}$ be the displacement of a particle from the origin at time t. Show that the particle travels in a circle of radius a at velocity $v=a\omega$ and with acceleration of magnitude $v^2/a$ directed toward the center of the circle.