imaginary number i - Printable Version +- Python Forum (https://python-forum.io) +-- Forum: Python Coding (https://python-forum.io/forum-7.html) +--- Forum: General Coding Help (https://python-forum.io/forum-8.html) +--- Thread: imaginary number i (/thread-35009.html) 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