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Re: Factoring

In your first expression, I cannot see what the symbols are after the 
"2*" inside the Sin function. To my eye it looks like it might be a 
"hatted" I followed by a period, but that makes no sense.

If that is supposed to be an I also, then expression you gave is 
real-valued (assuming that r is real):

   4 I r^2 Sin[2 I]  + I r^5 Sin[5 I
-4*r^2*Sinh[2] - r^5*Sinh[5]

If you prefer:

   TrigToExp[4 I r^2 Sin[2 I]  + I r^5 Sin[5 I]]
(2*r^2)/E^2 - 2*E^2*r^2 + r^5/(2*E^5) - (E^5*r^5)/2

In any event, for the last expression you gave, you could use:

   4x I Sin[t] + 28x^3 I Cos[t]
I*(28*x^3*Cos[t] + 4*x*Sin[t])

(I've converted the output cells to InputForm.)

I realize that the above does not respond to your more general question.

Matt wrote:
> Hello Mathgroup,
>   I'm sure that I've overlooked something obvious, but for the past two
> and a half hours, I've been trying to figure out how to use built-in
> Mathematica functions to just factor the imaginary number 'I' out of
> this:
> 4*I*r^2*Sin[2*θ] + I*r^5*Sin[5*θ]
> using Factor[] gives me I*r^2*(4*Sin[2*θ] + r^3*Sin[5*θ])
> using FactorTerms[] gives me I*(4*r^2*Sin[2*θ] + r^5*Sin[5*θ]) which
> is what I want, but as soon as I add in a common numerical factor, it
> also factors that out as well,
> e.g. 4*I*r^2*Sin[2*θ] + 8*I*r^5*Sin[5*θ]
> I finally just decided to divide the whole thing by 'I', and do some
> reconstruction of my expression, but I have the distinct feeling I've
> totally missed something very simple.  As an additional example, what
> if I just wanted to extract 2*x*I out of the following:
> 4*x*I*Sin[t] + 28*x^3*I*Cos[t]
> how would I do that?  In general, I'm looking for a function that says
> "Given an expression 'expr' and another expression 'sub' that is common
> to all additive terms of 'expr', give a result that is the product of
> 'sub' and the result of factoring 'sub' out of 'expr'".
> Thanks,
> Matt

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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