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To show that your expression is real you could use ComplexExpand. By default, ComplexExpand will expand a complex expression into its real and imaginary part under the assumption that all undefined symbols occurring in the expression are real. The only problem here is that as far as I know there is no way to provide extra assumptions to ComplexExpand, especially that ω and d are positive which means that Sqrt[ω] and Sqrt[d] are real as well. The easiest way around this is to replace these symbols with the square of another symbol, e.g.

Simplify[ComplexExpand[Im[finalnew /. {\[Omega]ω -> om^2, d -> dd^2}]], dd > 0]

which returns 0.

To show that your expression is real you could use ComplexExpand. By default, ComplexExpand will expand a complex expression into its real and imaginary part under the assumption that all undefined symbols occurring in the expression are real. The only problem here is that as far as I know there is no way to provide extra assumptions to ComplexExpand, especially that ω and d are positive which means that Sqrt[ω] and Sqrt[d] are real as well. The easiest way around this is to replace these symbols with the square of another symbol, e.g.

Simplify[ComplexExpand[Im[finalnew /. {\[Omega] -> om^2, d -> dd^2}]], dd > 0]

which returns 0.

To show that your expression is real you could use ComplexExpand. By default, ComplexExpand will expand a complex expression into its real and imaginary part under the assumption that all undefined symbols occurring in the expression are real. The only problem here is that as far as I know there is no way to provide extra assumptions to ComplexExpand, especially that ω and d are positive which means that Sqrt[ω] and Sqrt[d] are real as well. The easiest way around this is to replace these symbols with the square of another symbol, e.g.

Simplify[ComplexExpand[Im[finalnew /. {ω -> om^2, d -> dd^2}]], dd > 0]

which returns 0.

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Heike
Heike
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To show that your expression is real you could use ComplexExpand. By default, ComplexExpand will expand a complex expression into its real and imaginary part under the assumption that all undefined symbols occurring in the expression are real. The only problem here is that as far as I know there is no way to provide extra assumptions to ComplexExpand, especially that ω and d are positive which means that Sqrt[ω] and Sqrt[d] are real as well. The easiest way around this is to replace these symbols with the square of another symbol, e.g.

Simplify[ComplexExpand[Im[finalnew /. {\[Omega] -> om^2, d -> dd^2}]], dd > 0]

which returns 0.