Python Cmath Module
The cmath module provides access to mathematical functions for complex numbers. The functions in this module accept integers, floating-point numbers or complex numbers as arguments. They will also accept any Python object that has either a __complex__() or a __float__() method.
Importing the Module
import cmathConstants
The cmath module defines constants similar to math, but also includes complex infinity and NaN.
cmath.pi: The mathematical constant π.cmath.e: The mathematical constant e.cmath.tau: The mathematical constant τ.cmath.inf: Floating-point positive infinity.cmath.infj: Complex number with zero real part and positive infinity imaginary part.cmath.nan: Floating-point "not a number" (NaN) value.cmath.nanj: Complex number with zero real part and NaN imaginary part.
Coordinate Conversions
cmath.phase(x)
Return the phase of x (also known as the argument of x). This is the angle phi such that x = r * (cos(phi) + 1j * sin(phi)). The result is in the range [-π, π].
import cmath
z = 1 + 1j
print(cmath.phase(z)) # Output: 0.7853981633974483 (pi/4)cmath.polar(x)
Return the representation of x in polar coordinates. Returns a pair (r, phi) where r is the modulus of x and phi is the phase of x.
import cmath
z = 1 + 1j
r, phi = cmath.polar(z)
print(f"r: {r}, phi: {phi}")cmath.rect(r, phi)
Return the complex number x with polar coordinates r and phi. Equivalent to r * (math.cos(phi) + math.sin(phi)*1j).
import cmath
import math
z = cmath.rect(math.sqrt(2), math.pi / 4)
print(z) # Output: (1.0000000000000002+1j)Power and Logarithmic Functions
cmath.sqrt(x)
Return the square root of x. This works for negative real numbers as well, returning a complex result.
import cmath
print(cmath.sqrt(4)) # Output: (2+0j)
print(cmath.sqrt(-1)) # Output: 1jcmath.log(x[, base])
Returns the logarithm of x to the given base. If the base is not specified, returns the natural logarithm of x.
import cmath
print(cmath.log(cmath.e)) # Output: (1+0j)
print(cmath.log(-1)) # Output: 3.141592653589793j (pi * 1j)