from matplotlib import pyplot as plt
from matplotlib import ticker
import numpy as np
%matplotlib inline
x = np.arange(-3, 3, 0.01)
y = np.arange(-3, 3, 0.01)
X, Y = np.meshgrid(x, y)
Z = (X+ Y*1j)**1j
plt.contourf(X,Y,np.abs(Z), locator=ticker.LogLocator(base=2), cmap='PuBu')
formatter = ticker.ScalarFormatter()
plt.colorbar(format=formatter)
plt.gca().set_aspect('equal')
plt.title("absolute value of $i^i$")
plt.show()
plt.contourf(X,Y,np.angle(Z), cmap='PuBu')
plt.colorbar()
plt.gca().set_aspect('equal')
plt.title("angle of $i^i$")
plt.show()