import matplotlib.pyplot as plt
import numpy as np

fig, ax = plt.subplots()

ax.scatter([0], [0], color='red')
ax.text(0, -0.1, '0')

ax.scatter([0.5], [0], color='red')
ax.text(0.5, -0.1, '$z_0$')

ax.scatter([1], [1], color='red')
ax.text(1, 0.9, '$z_1$')

theta = np.linspace(-np.pi, np.pi, 100)
r = 0.2
x = r * np.cos(theta)
y = r * np.sin(theta)
ax.plot(x, y, color='black')
ax.text(0.17, -0.17, '$\gamma_0$')

ax.set_xlabel('Re z')
ax.set_ylabel('Im z')
ax.set_xlim([-2, 2])
ax.set_ylim([-2, 2])

ax.grid(True)
ax.set_aspect('equal', adjustable='box')
plt.show()