Chapter 7.2, Problem 9P

In Problems 7 to 10 you are given a complex function $z=f(t).$ In each case, show that a particle whose coordinate is (a) $x=\mathrm{Re}z,$ (b) $y=\mathrm{Im}z$ is undergoing simple harmonic motion, and find the amplitude, period, frequency, and velocity amplitude of the motion.

$z=2e^{i\pi t}$