creating complex numbers
a = 2 + 1j(2+1j)
print(a)<class 'complex'>
print(type(a))adding complex numbers
b = 2 - 3j(4-2j)
print(a + b)accessing real and imaginary parts
2.0
print(a.real)1.0
print(a.imag)magnitude of a complex number
2.23606797749979
print(abs(a))cmath---standard Python library for complex numbers
import cmathphase of a complex number (measured in radians)
0.4636476090008061
print(cmath.phase(a))Alternatively, convert complex numbers from rectangular to polar coordinates.
mag, angle = cmath.polar(a)(2+1j): magnitude = 2.23606797749979, angle = 0.4636476090008061
print('magnitude = {}, angle = {}'.format(mag, angle))Or convert from polar to rectangular coordinates
(2+1j)
print(cmath.rect(mag, angle))Multiplying complex numbers ...
(7-4j)
print(a * b)... is the same as multiplying the magnitudes and adding the phases
mag2 = abs(a) * abs(b)
angle2 = cmath.phase(a) + cmath.phase(b)(6.999999999999999-4j)
print(cmath.rect(mag2, angle2))import numpy as npcreating complex numpy arrays
c = np.array([1 + 2j, 3 + 1j, 4 - 5j], dtype=complex)[ 1.+2.j 3.+1.j 4.-5.j]
print(c)complex zeros
z = np.zeros(3, dtype=complex)[ 0.+0.j 0.+0.j 0.+0.j]
print(z)complex random numbers
import random
r = random.random() + random.random() * 1j(0.6589664597814023+0.23948971180747303j) as one possible result
print(r)magnitudes of a complex array
[ 2.23606798 3.16227766 6.40312424]
print(np.absolute(c))phases of a complex array
[ 1.10714872 0.32175055 -0.89605538]
print(np.angle(c))Indicator (or characterstic) function of a diminished seventh chord
P = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]FFT of the indicator function
F_P = np.fft.fft(P)[ 4.00000000e+00 +0.00000000e+00j -8.26946080e-16 +7.77156117e-16j
0.00000000e+00 +7.65713740e-16j 0.00000000e+00 +0.00000000e+00j
4.00000000e+00 -1.60410220e-15j -1.76491446e-15 +1.66533454e-15j
0.00000000e+00 +0.00000000e+00j -6.12323400e-17 -1.11022302e-16j
4.00000000e+00 -3.20820439e-15j 0.00000000e+00 +0.00000000e+00j
0.00000000e+00 +9.37968382e-16j 8.76736042e-16 +7.77156117e-16j]
print(F_P)Most of the values are 0 with miniscule floating-point errors. You can use
the numpy round function to round numpy array values (including complex
values) to a specified number of decimals.
[ 4.+0.j -0.+0.j 0.+0.j 0.+0.j 4.-0.j -0.+0.j 0.+0.j -0.-0.j 4.-0.j
0.+0.j 0.+0.j 0.+0.j]
print(np.round(F_P, 6))