Today I'm trying to prove the Euler's identity which is $e^{i\pi}+1=0$ by Python. My code is as follows:
euler = math.e
pi = np.pi
cos_pi = np.cos(pi)
sin_pi = np.sin(pi)
euler_id = euler**(imaginary*pi)
print((cos_pi+imaginary*sin_pi)+1)
print('e^(i*pi): %s' %eulers_id) # output = (-1+1.2246467991473532e-16j)
print('e^(i*pi)+1 =: %s' %(eulers_id+1)) # output = 1.2246467991473532e-16j
What I get is an imaginary number, did I do something wrong here? Thank you for your answer.