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Why I got complex answer while I know it should be real????

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Fatemeh Eslami
Fatemeh Eslami on 29 Jan 2013
Hi
I have a function to be solved. while I know it has a real answer I got complex answer, I check with 2 of my friends, one got real answer and the other one get the complex one as mine. what should I do? by the way,I want to solve it symbolic, This is the function and answer:
commands:
syms('x')
F=0.21*(exp(-0.157-0.157*x))-x
s=solve(F,x)
X=subs(s)
answer:
F = 21/(100*exp((157*x)/1000 + 157/1000)) - x
s =(1000*lambertw(0, -(100000*exp(157/1000))/3297))/157
X = 15.0552 +15.0159i
the answer tha my friend got with the same commands:
F =(21*exp(- (157*x)/1000 - 157/1000))/100 - x
s =(1000*lambertw(0, (3297*exp(-157/1000))/100000))/157
X = 0.1746

Accepted Answer

owr
owr on 29 Jan 2013
My guess, and this may be a long shot, is that somewhere along the way you took the sqrt of -1.
  1 Comment
Fatemeh Eslami
Fatemeh Eslami on 29 Jan 2013
thanks, but no, I dont. In fact, I have just write that one line command in my question.

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More Answers (2)

Shashank Prasanna
Shashank Prasanna on 29 Jan 2013
I got the same as your friend. Try the following
syms x F s X real
  3 Comments
Fatemeh Eslami
Fatemeh Eslami on 29 Jan 2013
Thanks Benji Bowbow,
this works:) syms x F s X real just I want to know that if in other cases that I am not sure about the complexity or reality of the answers,using this method gives me the correct answer or not.

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Walter Roberson
Walter Roberson on 29 Jan 2013
Both F are the same, but your solve() is returning the wrong answer. The lambertw argument is of the form A*exp(-B) but your solve() is instead forming 1/A * exp(B) .
Which MATLAB versions are the two of you running? Is one of you running with the Maple based symbolic toolbox, and the other running with the MuPAD based symbolic toolbox?
Note: complex values are not inherently wrong solutions. The general solution is not restricted to LambertW branch 0 the way the two solutions here show.

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