为什么Python中负数的平方根不是纯虚数？

Question

当我在 Python 中计算 (-1)**0.5 时，结果是 (6.123233995736766e-17+1j)。这个数字是多少，我怎样才能得到 1j 作为结果？

Answer 1

6.123233995736766e-17 是一个非常小的数字，用 scientific notation - written as a decimal, this number is 0.00000000000000006123233995736766. The correct real part of the result should be exactly zero, so the result is wrong, but only slightly wrong. Generally, computations involving floating-point numbers do not give exact results; for an explanation, see Is floating point math broken?

表示

如果您想计算复数平方根并保证负实数的平方根是纯虚数，您可以专门编写一个函数来实现此行为：

def my_sqrt(z):
    z = complex(z)
    if z.real < 0 and z.imag == 0:
        return 1j * (-z.real) ** 0.5
    else:
        return z ** 0.5

示例：

>>> my_sqrt(-1)
1j
>>> my_sqrt(-2)
1.4142135623730951j
>>> my_sqrt(9)
(3+0j)
>>> my_sqrt(-3 + 4j)
(1.0000000000000002+2j)

请注意，由于浮点数不准确，某些结果会略有错误，例如 -3 + 4j 的真实平方根应该是 1 + 2j。如果您想在所有可能的情况下都获得准确的结果，请考虑学习 SymPy.

为什么Python中负数的平方根不是纯虚数？

Why is the square root of a negative number not purely imaginary in Python?

python

complex-numbers