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?

from numpy import sqrt
arr = sqrt(-1)
print(arr)

Not sure about numpy but in pure python you can use `cmath.sqrt(-1)`. — Ashwini Chaudhary, Jul 20 '13 at 21:26
Maybe this is beside the point, but I can't reproduce that issue exactly. I get `RuntimeWarning: invalid value encountered in sqrt` on the calculation, then `nan` is printed (which is a `numpy.float64`, to be clear). — wjandrea, Jan 20 '22 at 22:14

score 32 · Answer 1 · answered Jul 20 '13 at 21:54

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

score 18 · Answer 2 · answered Feb 06 '14 at 12:47

18

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

answered Feb 06 '14 at 12:47

David Zwicker

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This is an overall better answer in 2020. – logicOnAbstractions Mar 08 '20 at 20:14

score 12 · Accepted Answer · edited Jul 16 '18 at 00:55

12

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

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

edited Jul 16 '18 at 00:55

dbliss

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answered Jul 20 '13 at 22:33

John La Rooy

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score 0 · Answer 4 · answered Jul 20 '13 at 21:20

0

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

answered Jul 20 '13 at 21:20

Marcin

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My guess is that @marriam is already using numpy, because `np.sqrt(-1)` results in the `invalid value encountered...` warning, while `math.sqrt(-1)` results in `ValueError: math domain error`. – Warren Weckesser Jul 20 '13 at 22:00
@WarrenWeckesser Either way, an appreciation of what complex numbers are will help her. – Marcin Jul 20 '13 at 22:01

score 0 · Answer 5 · answered Jul 20 '13 at 23:21

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.

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

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