How can I take the square root of -1 using python?

Question

When I take the square root of -1 it gives me an error:

invalid value encountered in sqrt

How do I fix that?

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Answer 1

The square root of -1 is not a real number, but rather an imaginary number. IEEE 754 does not have a way of representing imaginary numbers.

numpy has support for complex numbers. I suggest you use that: http://docs.scipy.org/doc/numpy/user/basics.types.html

Answer 2

You need to use the sqrt from the cmath module (part of the standard library)

>>> import cmath
>>> cmath.sqrt(-1)
1j

Answer 3

Others have probably suggested more desirable methods, but just to add to the conversation, you could always multiply any number less than 0 (the value you want the sqrt of, -1 in this case) by -1, then take the sqrt of that. Just know then that your result is imaginary.

Answer 4

I just discovered the convenience function numpy.lib.scimath.sqrt explained in the sqrt documentation. I use it as follows:

>>> from numpy.lib.scimath import sqrt as csqrt
>>> csqrt(-1)
1j

Answer 5

To avoid the invalid value warning/error, the argument to numpy's sqrt function must be complex:

In [8]: import numpy as np

In [9]: np.sqrt(-1+0j)
Out[9]: 1j

As @AshwiniChaudhary pointed out in a comment, you could also use the cmath standard library:

In [10]: cmath.sqrt(-1)
Out[10]: 1j