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imaginary number i - mr_byte31 - Sep-23-2021

I was trying the following commands :

>>> -1 ** 0.5
-1.0
>>> (-1) ** 0.5
(6.123233995736766e-17+1j)
I was expecting "1j" , "1i" or "i"


I am just surprised to find different values for the same problem.

I was expecting to see that python has higher priority of "sign" over the power "**"

any reason for those results?


RE: imaginary number i - bowlofred - Sep-23-2021

The second one is 1j to within the precision of the computation. Floating point math isn't necessarily exact. https://docs.python.org/3/tutorial/floatingpoint.html


RE: imaginary number i - deanhystad - Sep-23-2021

The reason -1**0.5 == -1 is that ** has higher precedence than unary -.

The reason (-1)**5 ~= 1j is that the parenthesis change the order of operations. Unary - is first, then **. As for the small remainder,
you don't need imaginary numbers to see that you cannot represent an infinite set of numbers using a limited set of bytes.


RE: imaginary number i - mr_byte31 - Sep-23-2021

then why the first one not correct??

>>> -1 ** 0.5
-1.0



RE: imaginary number i - jefsummers - Sep-23-2021

The first one IS correct.
The square root of 1 is 1
Then apply the unary minus and you get -1


RE: imaginary number i - bowlofred - Sep-23-2021

(Sep-23-2021, 04:01 PM)mr_byte31 Wrote: then why the first one not correct??

>>> -1 ** 0.5
-1.0

As mentioned, the precedence rules mean the exponentiation happens first. The effect is the same as
- (1 ** 0.5)
Operator precedence


RE: imaginary number i - deanhystad - Sep-23-2021

It gets really confusing when it looks like Python can exactly represent all the numbers involved. Why is 0.3 not 0.3?
print(0.1, 0.2, 0.1 + 0.2, 0.3)
Output:
0.1 0.2 0.30000000000000004 0.3



RE: imaginary number i - mr_byte31 - Sep-23-2021

(Sep-23-2021, 03:59 PM)deanhystad Wrote: The reason -1**0.5 == -1 is that ** has higher precedence than unary -.

The reason (-1)**5 ~= 1j is that the parenthesis change the order of operations. Unary - is first, then **. As for the small remainder,
you don't need imaginary numbers to see that you cannot represent an infinite set of numbers using a limited set of bytes.

This is the first programming language that I see to give priority to "power" than to sign "-"


RE: imaginary number i - buran - Sep-23-2021

(Sep-23-2021, 04:28 PM)mr_byte31 Wrote: This is the first programming language that I see to give priority to "power" than to sign "-"

https://math.stackexchange.com/q/1299236

And one of the answers gives an example - FORTRAN
Same precedence in Matlab - https://www.mathworks.com/help/matlab/matlab_prog/operator-precedence.html