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Topic: ComplexExpand off by a factor of (-1)?
Replies: 3   Last Post: Feb 23, 2013 7:01 AM

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 Bob Hanlon Posts: 695 Registered: 10/29/11
Re: ComplexExpand off by a factor of (-1)?
Posted: Feb 23, 2013 7:01 AM

expr = (E^(I*y) - E^(-I*y))/2*I;

If you plot your expression it is clear that it is -Sin[y] rather than Sin[y]

Plot[expr, {y, -Pi, Pi}]

ComplexExpand[expr]

-Sin[y]

Term-by-term comparison in power series

Assuming[{Element[n, Integers]},
SeriesCoefficient[expr, {y, 0, n}] ==
SeriesCoefficient[-Sin[y], {y, 0, n}] //
FullSimplify]

True

Bob Hanlon

On Fri, Feb 22, 2013 at 1:05 AM, <charles.ces@gmail.com> wrote:
> Would someone be able to help me understand why when I enter the expression:
>
> ComplexExpand[(E^(I*y) - E^(-I*y))/2*I] I get a result of -Sin[y] instead of Sin[y]?
>
> Thanks.
>
> Charles S.
>

Date Subject Author
2/23/13 Bob Hanlon
2/23/13 Murray Eisenberg
2/23/13 Raul Martinez