#!/usr/bin/python3

import numpy as np
import matplotlib as mp
import matplotlib.pyplot as plt

x = np.arange(-np.pi, np.pi, np.pi/360)
ys = np.imag(np.exp(1j*x))
yc = np.real(np.exp(1j*x))

plt.axis([-np.pi, np.pi, -1.2, 1.2])
plt.title(r"$e^{-i\theta}=\cos(\theta)+i\,\sin(\theta)$", fontsize=20)
plt.xlabel(r"$\theta$ [rad]", fontsize=20, fontname="serif")
plt.ylabel("value", fontsize=20, fontname='serif')

plt.plot(x, ys)
plt.plot(x, yc)
plt.show()