ilaplace confusing - result from command window and from m file gui is not the same

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john
john 2014-1-20
编辑： john 2014-2-27
Hi,
I write in command window:
ilaplace((0.99984898859777815438576453743735*s^2 + 1414.0*s - 414151.01140222184561423546256265)/((s + 1000.0)*(s^2 + 1000000.0)))
And I got : ans =
(199002808534433793169*cos(1000*t))/140737488355328000000 - 58286573144567511919/(140737488355328000000*exp(1000*t)) - (1169*sin(1000*t))/140737488355328000000
I write the same in m file from GUI and I got:
0.707*exp(1000.0*t*i) - 0.41415101140222184561423546256265/exp(1000.0*t) + 0.707*(1/exp(1000.0*t*i))
WHY I GOT COMPLEX NUMBER? "i"?

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采纳的回答

Mischa Kim
Mischa Kim 2014-1-21
编辑：Mischa Kim 2014-1-21
Hello John, it is actually the same. Try plotting the two results.
The reason you get complex numbers is because of Euler's formula:
exp^(ix) = cos(x) + i*sin(x)
If you analyze the results you'll see that you get (really) small imaginary numbers. That's because the computation is done in floating point arithmetic (see this answer). In case you are not comfortable with the imaginary parts, just plot the real parts.
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john
john 2014-2-25
编辑：john 2014-2-27
Sorry, but for relative little number simplify doesn't help.
In command window I it is OK, I get:
>> r=simplify(ilaplace(-((4280819729186186979044460847261*s^2)/51422017416287688817342786954917203280710495801049370729644032 + (994733177774077628149071673933*s)/50216813883093446110686315385661331328818843555712276103168 - 949357667952072971550917252451/1569275433846670190958947355801916604025588861116008628224)/((3*s + 200)*(s^2 + 98596))))
r =
19981467697883435869/(3970734387895709337413208929317684822969348320657408*exp((200*t)/3)) - (694227838351497933185*cos(314*t))/21177250068777116466203780956360985722503191043506176 - (11693735405742169632973*sin(314*t))/831207065199501821298498402537168689608250248457617408
But in guide I get:
r=simplify(ilaplace(-((4280819729186186979044460847261*s^2)/51422017416287688817342786954917203280710495801049370729644032 + (994733177774077628149071673933*s)/50216813883093446110686315385661331328818843555712276103168 - 949357667952072971550917252451/1569275433846670190958947355801916604025588861116008628224)/((3*s + 200)*(s^2 + 98596))))
r =
3.0679013785265445477520983725365*10^(-35)*dirac(t)
Why? It is sooo bad!

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