Why do I get the wrong value when I try to evaluate log([-1;1]) this way?

Question

Farouk Moukaddem 2017-11-9

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回答： Viggnesh Venkatakrishnan 2018-12-17

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I get different results in MATLAB R2017a when I perform the same operation in different ways:

>> v = -1 + 1i; >> log([0;0]./v-1)

ans =

   0.0000 - 3.1416i
   0.0000 - 3.1416i

This is incorrect

On the other hand, doing the following shows correct output: >> log([0;0]./(-1 + 1i)-1)

ans =

   0.0000 + 3.1416i
   0.0000 + 3.1416i

This is correct

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Star Strider 2017-11-9

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It was apparently fixed in R2017b:

v = -1 + 1i;
log([0;0]./v-1)
log([0;0]./(-1 + 1i)-1)
ans =
              0 +     3.1416i
              0 +     3.1416i
ans =
              0 +     3.1416i
              0 +     3.1416i

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Answer 1

Viggnesh Venkatakrishnan 2018-12-17

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Hi Farouk,

I understand that you are getting different results in MATLAB R2017a when you perform the below operation in different ways:

% way 1
>> v = -1 + 1i; >> log([0;0]./v-1)
% way 2
>> log([0;0]./(-1 + 1i)-1)

This is a known issue with MATLAB R2017a where there is inconsistency in handling real values stored in a complex array for log, log2, log10, and log1p. This is a link to the External Bug Report : https://www.mathworks.com/support/bugreports/details/1653779

This issue has been fixed in R2017b.

Thanks and Regards,

Viggnesh Venkatakrishnan

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Answer 2

Roger Stafford 2017-11-9

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编辑：Roger Stafford 2017-11-9

Both answers are correct for log(-1). In fact there are infinitely many possible correct answers of the form (2*n+1)*pi*i for any integer n, positive or negative. In mathematics the logarithm function is said to have infinitely many “branches”. If you started with z = 1 and moved z continuously in the complex plane in a circle around the origin as center in the counterclockwise direction you would arrive at pi*i for log(-1). However, if you moved clockwise instead, you would arrive at -pi*i. If you continued around multiple times you would get all those other possible values.