Re: ComplexExpand off by a factor of (-1)?

• To: mathgroup at smc.vnet.net
• Subject: [mg129889] Re: ComplexExpand off by a factor of (-1)?
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 23 Feb 2013 07:01:26 -0500 (EST)
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• References: <20130222060524.703B768D0@smc.vnet.net>

```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 at 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.
>

```

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