Problem with cubic root

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Chesus
Chesus 2023-9-10
评论： Bruno Luong 2023-9-11
Ran in:
When I try to get the cubic root of -1 (which should be -1) I get this:
(-1).^(1/3)
ans = 0.5000 + 0.8660i
How do I fix this?
  1 个评论
Dyuman Joshi
Dyuman Joshi 2023-9-10
What is there to fix? That is one of the 3 cube roots of -1.
Do you wish to obtain -1 as the output?

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采纳的回答

Sam Chak
Sam Chak 2023-9-10
Ran in:
nthroot(-1, 3)
ans = -1
  4 个评论
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Walter Roberson
Walter Roberson 2023-9-10
编辑：Walter Roberson 2023-9-10
Ran in:
@Bruno Luong
I put in the condition that when A is negative
A = -rand(1,1e6) * 100000;
l1 = log(A);
l2 = log(-A) + log(-1);
nnz(l1 ~= l2)
ans = 0
Bit for bit equality.
Bruno Luong
Bruno Luong 2023-9-11
I know it is true for negative A, but readers might wonder out the blue where this come from: "log(A) is log(-A)+log(-1)"?
And next why log(-1) is 1i*pi (and not -1i*pi)? Of course one can check it with MATLAB command.
The MATLAB log doc states
log(A) = log(abs(A)) + 1i*angle(A)
why not start with that?
And btw log(A) = log(abs(A)) + 1i*angle(A) is not entirely true either in some special values of A.

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