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edited Nov 23, 2017 at 18:50

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(\[Pi]π (4 c^3 ks^3 \[Tau]^2τ^2 Sqrt[-2 I - \[Tau]τ \[Omega]]ω] Sqrt[ 2 I - \[Tau]τ \[Omega]]ω] + \[Omega]^2ω^2 (4 + \[Tau]^2τ^2 \[Omega]^2ω^2) \ (2 Sqrt[(\[Tau]τ (2 I - \[Tau]τ \[Omega]ω))/\[Omega]]ω] - I \[Tau]^τ^(3/2) Sqrt[\[Omega]Sqrt[ω (2 I - \[Tau]τ \[Omega]ω)] + 2 Sqrt[-((\[Tau]τ (2 I + \[Tau]τ \[Omega]ω))/\[Omega]ω)] + I \[Tau]τ \[Omega]ω Sqrt[-((\[Tau]τ (2 I + \[Tau]τ \[Omega]ω))/\ \[Omega]ω)]) + c^2 ks^2 \[Tau]τ \[Omega]ω (4 I Sqrt[(\[Tau]τ (2 I - \[Tau]τ \ \[Omega]ω))/\[Omega]]ω] + 4 \[Tau]^τ^(3/2) Sqrt[\[Omega]Sqrt[ω (2 I - \[Tau]τ \[Omega]ω)] - 4 I Sqrt[-((\[Tau]τ (2 I + \[Tau]τ \[Omega]ω))/\[Omega]ω)] + 4 \[Tau]τ \[Omega]ω Sqrt[-((\[Tau]τ (2 I + \[Tau]τ \[Omega]ω))/\ \[Omega]ω)] + I \[Tau]^τ^(5/2) \[Omega]^ω^( 3/2) (Sqrt[-2 I - \[Tau]τ \[Omega]]ω] - Sqrt[ 2 I - \[Tau]τ \[Omega]]ω]))))/(8 c \[Tau]^2τ^2 Sqrt[-2 I - \ \[Tau]τ \[Omega]]ω] Sqrt[ 2 I - \[Tau]τ \[Omega]]ω] (c^4 ks^4 \[Tau]^2τ^2 + 4 \[Omega]^2ω^2 + 2 c^2 ks^2 \[Tau]^2τ^2 \[Omega]^2ω^2 + \[Tau]^2τ^2 \[Omega]^4ω^4))

FullSimplify[ ComplexExpand[ Im[(\[Pi]π (4 c^3 ks^3 \[Tau]^2τ^2 Sqrt[-2 I - \[Tau]τ \[Omega]]ω] Sqrt[ 2 I - \[Tau]τ \[Omega]]ω] + \[Omega]^2ω^2 (4 + \[Tau]^2τ^2 \ \[Omega]^2ω^2) (2 Sqrt[(\[Tau]τ (2 I - \[Tau]τ \[Omega]ω))/\[Omega]]ω] - I \[Tau]^τ^(3/2) Sqrt[\[Omega]Sqrt[ω (2 I - \[Tau]τ \[Omega]ω)] + 2 Sqrt[-((\[Tau]τ (2 I + \[Tau]τ \[Omega]ω))/\[Omega]ω)] + I \[Tau]τ \[Omega]ω Sqrt[-((\[Tau]τ (2 I + \[Tau]τ \[Omega]ω))/\ \[Omega]ω)]) + c^2 ks^2 \[Tau]τ \[Omega]ω (4 I Sqrt[(\[Tau]τ (2 I - \[Tau]τ \ \[Omega]ω))/\[Omega]]ω] + 4 \[Tau]^τ^(3/2) Sqrt[\[Omega]Sqrt[ω (2 I - \[Tau]τ \[Omega]ω)] - 4 I Sqrt[-((\[Tau]τ (2 I + \[Tau]τ \[Omega]ω))/\[Omega]ω)] + 4 \[Tau]τ \[Omega]ω Sqrt[-((\[Tau]τ (2 I + \[Tau]τ \[Omega]ω))/\ \[Omega]ω)] + I \[Tau]^τ^(5/2) \[Omega]^ω^( 3/2) (Sqrt[-2 I - \[Tau]τ \[Omega]]ω] - Sqrt[ 2 I - \[Tau]τ \[Omega]]ω]))))/(8 c \[Tau]^2τ^2 Sqrt[-2 I - \ \[Tau]τ \[Omega]]ω] Sqrt[ 2 I - \[Tau]τ \[Omega]]ω] (c^4 ks^4 \[Tau]^2τ^2 + 4 \[Omega]^2ω^2 + 2 c^2 ks^2 \[Tau]^2τ^2 \[Omega]^2ω^2 + \[Tau]^2τ^2 \[Omega]^4ω^4))], TargetFunctions -> {Re, Im}], {ks > 0, \[Omega]ω > 0, \[Tau]τ > 0, c > 0}]

(\[Pi] (4 c^3 ks^3 \[Tau]^2 Sqrt[-2 I - \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] + \[Omega]^2 (4 + \[Tau]^2 \[Omega]^2) \ (2 Sqrt[(\[Tau] (2 I - \[Tau] \[Omega]))/\[Omega]] - I \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] + 2 Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + I \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])]) + c^2 ks^2 \[Tau] \[Omega] (4 I Sqrt[(\[Tau] (2 I - \[Tau] \ \[Omega]))/\[Omega]] + 4 \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] - 4 I Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + 4 \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])] + I \[Tau]^(5/2) \[Omega]^( 3/2) (Sqrt[-2 I - \[Tau] \[Omega]] - Sqrt[ 2 I - \[Tau] \[Omega]]))))/(8 c \[Tau]^2 Sqrt[-2 I - \ \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] (c^4 ks^4 \[Tau]^2 + 4 \[Omega]^2 + 2 c^2 ks^2 \[Tau]^2 \[Omega]^2 + \[Tau]^2 \[Omega]^4))

FullSimplify[ ComplexExpand[ Im[(\[Pi] (4 c^3 ks^3 \[Tau]^2 Sqrt[-2 I - \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] + \[Omega]^2 (4 + \[Tau]^2 \ \[Omega]^2) (2 Sqrt[(\[Tau] (2 I - \[Tau] \[Omega]))/\[Omega]] - I \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] + 2 Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + I \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])]) + c^2 ks^2 \[Tau] \[Omega] (4 I Sqrt[(\[Tau] (2 I - \[Tau] \ \[Omega]))/\[Omega]] + 4 \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] - 4 I Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + 4 \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])] + I \[Tau]^(5/2) \[Omega]^( 3/2) (Sqrt[-2 I - \[Tau] \[Omega]] - Sqrt[ 2 I - \[Tau] \[Omega]]))))/(8 c \[Tau]^2 Sqrt[-2 I - \ \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] (c^4 ks^4 \[Tau]^2 + 4 \[Omega]^2 + 2 c^2 ks^2 \[Tau]^2 \[Omega]^2 + \[Tau]^2 \[Omega]^4))], TargetFunctions -> {Re, Im}], {ks > 0, \[Omega] > 0, \[Tau] > 0, c > 0}]

(π (4 c^3 ks^3 τ^2 Sqrt[-2 I - τ ω] Sqrt[ 2 I - τ ω] + ω^2 (4 + τ^2 ω^2) \ (2 Sqrt[(τ (2 I - τ ω))/ω] - I τ^(3/2) Sqrt[ω (2 I - τ ω)] + 2 Sqrt[-((τ (2 I + τ ω))/ω)] + I τ ω Sqrt[-((τ (2 I + τ ω))/\ ω)]) + c^2 ks^2 τ ω (4 I Sqrt[(τ (2 I - τ \ ω))/ω] + 4 τ^(3/2) Sqrt[ω (2 I - τ ω)] - 4 I Sqrt[-((τ (2 I + τ ω))/ω)] + 4 τ ω Sqrt[-((τ (2 I + τ ω))/\ ω)] + I τ^(5/2) ω^( 3/2) (Sqrt[-2 I - τ ω] - Sqrt[ 2 I - τ ω]))))/(8 c τ^2 Sqrt[-2 I - \ τ ω] Sqrt[ 2 I - τ ω] (c^4 ks^4 τ^2 + 4 ω^2 + 2 c^2 ks^2 τ^2 ω^2 + τ^2 ω^4))

FullSimplify[ ComplexExpand[ Im[(π (4 c^3 ks^3 τ^2 Sqrt[-2 I - τ ω] Sqrt[ 2 I - τ ω] + ω^2 (4 + τ^2 \ ω^2) (2 Sqrt[(τ (2 I - τ ω))/ω] - I τ^(3/2) Sqrt[ω (2 I - τ ω)] + 2 Sqrt[-((τ (2 I + τ ω))/ω)] + I τ ω Sqrt[-((τ (2 I + τ ω))/\ ω)]) + c^2 ks^2 τ ω (4 I Sqrt[(τ (2 I - τ \ ω))/ω] + 4 τ^(3/2) Sqrt[ω (2 I - τ ω)] - 4 I Sqrt[-((τ (2 I + τ ω))/ω)] + 4 τ ω Sqrt[-((τ (2 I + τ ω))/\ ω)] + I τ^(5/2) ω^( 3/2) (Sqrt[-2 I - τ ω] - Sqrt[ 2 I - τ ω]))))/(8 c τ^2 Sqrt[-2 I - \ τ ω] Sqrt[ 2 I - τ ω] (c^4 ks^4 τ^2 + 4 ω^2 + 2 c^2 ks^2 τ^2 ω^2 + τ^2 ω^4))], TargetFunctions -> {Re, Im}], {ks > 0, ω > 0, τ > 0, c > 0}]

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edit approved Nov 23, 2017 at 12:35

Bettertomo

([Pi] (4 c^3 ks^3 [Tau]^2 Sqrt[-2 I - [Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] + [Omega]^2 (4 + [Tau]^2 [Omega]^2)
(2 Sqrt[([Tau] (2 I - [Tau] [Omega]))/[Omega]] - I [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] + 2 Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + I [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])]) + c^2 ks^2 [Tau] [Omega] (4 I Sqrt[([Tau] (2 I - [Tau]
[Omega]))/[Omega]] + 4 [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] - 4 I Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + 4 [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])] + I [Tau]^(5/2) [Omega]^( 3/2) (Sqrt[-2 I - [Tau] [Omega]] - Sqrt[ 2 I - [Tau] [Omega]]))))/(8 c [Tau]^2 Sqrt[-2 I -
[Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] (c^4 ks^4 [Tau]^2 + 4 [Omega]^2 + 2 c^2 ks^2 [Tau]^2 [Omega]^2 + [Tau]^2 [Omega]^4))

(\[Pi] (4 c^3 ks^3 \[Tau]^2 Sqrt[-2 I - \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] + \[Omega]^2 (4 + \[Tau]^2 \[Omega]^2) \ (2 Sqrt[(\[Tau] (2 I - \[Tau] \[Omega]))/\[Omega]] - I \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] + 2 Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + I \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])]) + c^2 ks^2 \[Tau] \[Omega] (4 I Sqrt[(\[Tau] (2 I - \[Tau] \ \[Omega]))/\[Omega]] + 4 \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] - 4 I Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + 4 \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])] + I \[Tau]^(5/2) \[Omega]^( 3/2) (Sqrt[-2 I - \[Tau] \[Omega]] - Sqrt[ 2 I - \[Tau] \[Omega]]))))/(8 c \[Tau]^2 Sqrt[-2 I - \ \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] (c^4 ks^4 \[Tau]^2 + 4 \[Omega]^2 + 2 c^2 ks^2 \[Tau]^2 \[Omega]^2 + \[Tau]^2 \[Omega]^4))

([Pi] (4 c^3 ks^3 [Tau]^2 Sqrt[-2 I - [Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] + [Omega]^2 (4 + [Tau]^2 [Omega]^2)
(2 Sqrt[([Tau] (2 I - [Tau] [Omega]))/[Omega]] - I [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] + 2 Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + I [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])]) + c^2 ks^2 [Tau] [Omega] (4 I Sqrt[([Tau] (2 I - [Tau]
[Omega]))/[Omega]] + 4 [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] - 4 I Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + 4 [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])] + I [Tau]^(5/2) [Omega]^( 3/2) (Sqrt[-2 I - [Tau] [Omega]] - Sqrt[ 2 I - [Tau] [Omega]]))))/(8 c [Tau]^2 Sqrt[-2 I -
[Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] (c^4 ks^4 [Tau]^2 + 4 [Omega]^2 + 2 c^2 ks^2 [Tau]^2 [Omega]^2 + [Tau]^2 [Omega]^4))

(\[Pi] (4 c^3 ks^3 \[Tau]^2 Sqrt[-2 I - \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] + \[Omega]^2 (4 + \[Tau]^2 \[Omega]^2) \ (2 Sqrt[(\[Tau] (2 I - \[Tau] \[Omega]))/\[Omega]] - I \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] + 2 Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + I \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])]) + c^2 ks^2 \[Tau] \[Omega] (4 I Sqrt[(\[Tau] (2 I - \[Tau] \ \[Omega]))/\[Omega]] + 4 \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] - 4 I Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + 4 \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])] + I \[Tau]^(5/2) \[Omega]^( 3/2) (Sqrt[-2 I - \[Tau] \[Omega]] - Sqrt[ 2 I - \[Tau] \[Omega]]))))/(8 c \[Tau]^2 Sqrt[-2 I - \ \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] (c^4 ks^4 \[Tau]^2 + 4 \[Omega]^2 + 2 c^2 ks^2 \[Tau]^2 \[Omega]^2 + \[Tau]^2 \[Omega]^4))

added 1255 characters in body

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edited Nov 23, 2017 at 9:07

user64494

Addition 1.

([Pi] (4 c^3 ks^3 [Tau]^2 Sqrt[-2 I - [Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] + [Omega]^2 (4 + [Tau]^2 [Omega]^2)
(2 Sqrt[([Tau] (2 I - [Tau] [Omega]))/[Omega]] - I [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] + 2 Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + I [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])]) + c^2 ks^2 [Tau] [Omega] (4 I Sqrt[([Tau] (2 I - [Tau]
[Omega]))/[Omega]] + 4 [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] - 4 I Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + 4 [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])] + I [Tau]^(5/2) [Omega]^( 3/2) (Sqrt[-2 I - [Tau] [Omega]] - Sqrt[ 2 I - [Tau] [Omega]]))))/(8 c [Tau]^2 Sqrt[-2 I -
[Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] (c^4 ks^4 [Tau]^2 + 4 [Omega]^2 + 2 c^2 ks^2 [Tau]^2 [Omega]^2 + [Tau]^2 [Omega]^4))

Addition 2. In fact, the imaginary part is zero up to

FullSimplify[ ComplexExpand[ Im[(\[Pi] (4 c^3 ks^3 \[Tau]^2 Sqrt[-2 I - \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] + \[Omega]^2 (4 + \[Tau]^2 \ \[Omega]^2) (2 Sqrt[(\[Tau] (2 I - \[Tau] \[Omega]))/\[Omega]] - I \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] + 2 Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + I \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])]) + c^2 ks^2 \[Tau] \[Omega] (4 I Sqrt[(\[Tau] (2 I - \[Tau] \ \[Omega]))/\[Omega]] + 4 \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] - 4 I Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + 4 \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])] + I \[Tau]^(5/2) \[Omega]^( 3/2) (Sqrt[-2 I - \[Tau] \[Omega]] - Sqrt[ 2 I - \[Tau] \[Omega]]))))/(8 c \[Tau]^2 Sqrt[-2 I - \ \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] (c^4 ks^4 \[Tau]^2 + 4 \[Omega]^2 + 2 c^2 ks^2 \[Tau]^2 \[Omega]^2 + \[Tau]^2 \[Omega]^4))], TargetFunctions -> {Re, Im}], {ks > 0, \[Omega] > 0, \[Tau] > 0, c > 0}]

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Addition.

([Pi] (4 c^3 ks^3 [Tau]^2 Sqrt[-2 I - [Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] + [Omega]^2 (4 + [Tau]^2 [Omega]^2)
(2 Sqrt[([Tau] (2 I - [Tau] [Omega]))/[Omega]] - I [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] + 2 Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + I [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])]) + c^2 ks^2 [Tau] [Omega] (4 I Sqrt[([Tau] (2 I - [Tau]
[Omega]))/[Omega]] + 4 [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] - 4 I Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + 4 [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])] + I [Tau]^(5/2) [Omega]^( 3/2) (Sqrt[-2 I - [Tau] [Omega]] - Sqrt[ 2 I - [Tau] [Omega]]))))/(8 c [Tau]^2 Sqrt[-2 I -
[Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] (c^4 ks^4 [Tau]^2 + 4 [Omega]^2 + 2 c^2 ks^2 [Tau]^2 [Omega]^2 + [Tau]^2 [Omega]^4))

Addition 1.

([Pi] (4 c^3 ks^3 [Tau]^2 Sqrt[-2 I - [Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] + [Omega]^2 (4 + [Tau]^2 [Omega]^2)
(2 Sqrt[([Tau] (2 I - [Tau] [Omega]))/[Omega]] - I [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] + 2 Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + I [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])]) + c^2 ks^2 [Tau] [Omega] (4 I Sqrt[([Tau] (2 I - [Tau]
[Omega]))/[Omega]] + 4 [Tau]^(3/2) Sqrt[[Omega] (2 I - [Tau] [Omega])] - 4 I Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/[Omega])] + 4 [Tau] [Omega] Sqrt[-(([Tau] (2 I + [Tau] [Omega]))/
[Omega])] + I [Tau]^(5/2) [Omega]^( 3/2) (Sqrt[-2 I - [Tau] [Omega]] - Sqrt[ 2 I - [Tau] [Omega]]))))/(8 c [Tau]^2 Sqrt[-2 I -
[Tau] [Omega]] Sqrt[ 2 I - [Tau] [Omega]] (c^4 ks^4 [Tau]^2 + 4 [Omega]^2 + 2 c^2 ks^2 [Tau]^2 [Omega]^2 + [Tau]^2 [Omega]^4))

Addition 2. In fact, the imaginary part is zero up to

FullSimplify[ ComplexExpand[ Im[(\[Pi] (4 c^3 ks^3 \[Tau]^2 Sqrt[-2 I - \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] + \[Omega]^2 (4 + \[Tau]^2 \ \[Omega]^2) (2 Sqrt[(\[Tau] (2 I - \[Tau] \[Omega]))/\[Omega]] - I \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] + 2 Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + I \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])]) + c^2 ks^2 \[Tau] \[Omega] (4 I Sqrt[(\[Tau] (2 I - \[Tau] \ \[Omega]))/\[Omega]] + 4 \[Tau]^(3/2) Sqrt[\[Omega] (2 I - \[Tau] \[Omega])] - 4 I Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\[Omega])] + 4 \[Tau] \[Omega] Sqrt[-((\[Tau] (2 I + \[Tau] \[Omega]))/\ \[Omega])] + I \[Tau]^(5/2) \[Omega]^( 3/2) (Sqrt[-2 I - \[Tau] \[Omega]] - Sqrt[ 2 I - \[Tau] \[Omega]]))))/(8 c \[Tau]^2 Sqrt[-2 I - \ \[Tau] \[Omega]] Sqrt[ 2 I - \[Tau] \[Omega]] (c^4 ks^4 \[Tau]^2 + 4 \[Omega]^2 + 2 c^2 ks^2 \[Tau]^2 \[Omega]^2 + \[Tau]^2 \[Omega]^4))], TargetFunctions -> {Re, Im}], {ks > 0, \[Omega] > 0, \[Tau] > 0, c > 0}]

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added 1034 characters in body

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edited Nov 23, 2017 at 8:52

user64494

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answered Nov 23, 2017 at 7:44

user64494