math - Wrong value for cube root in Python

Question

Using Python 3.5 both at repl.it and the console in Windows, I get wrong answers for cube roots.

When the input is (-1)**(1/3), I get the complex number (0.5000000000000001+0.8660254037844386j) as the answer when it should simply be -1. Any negative value under this root seems to give a complex result.

Am I doing something wrong?

Answer 1

Exponentiation with negative bases typically involves complex numbers, so Python switches to complex numbers when it sees the negative base. Such exponentiation is typically mutlivalued, and Python doesn't always return the value you might expect.

For the special case of the 1/3 power with real bases, you could write a function like this:

def cubeRoot(x):
    if x >= 0:
        return x**(1/3)
    else:
        return -(-x)**(1/3)

Which will give the expected real cube root.