The cmath.log() function returns the natural logarithm of a given complex number.

cmath.log(x[, base])
x The value(real or complex) whose logarithm we want. If the argument is a real number, it is first converted to a complex number before the operation.
base This optional argument indicates the base to be used in calculating the logarithm. If the base is not specified,  natural logarithm (base e) is used.

The function returns a complex number representing the logarithm of to the given base. 

import cmath

print(cmath.log(2 + 3j))
print(cmath.log(1 + 0.5j))
print(cmath.log(10 + -10j))