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I want to evaluate the following expression

Arg[E^((0. + 6.66667*10^-12 I) omega)/(4 - E^((0. + 2.*10^-11 I) omega))]

where the variable omega is real and positive.

I have tried

$Assumptions = {omega \[Element] Reals, omega > 0}
Simplify[ComplexExpand[expression above]]

But it does not work. What am I doing wrong?

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1 Answer 1

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Give ComplexExpand a TargetFunctions option, and use FullSimplify instead:

FullSimplify[
    ComplexExpand[
        Arg[E^((0.+6.66667*10^-12 I) omega)/(4-E^((0.+2.*10^-11 I) omega))],
        TargetFunctions -> {Re, Im}
    ],
    omega \[Element] Reals && omega > 0
]

ArcTan[4. Cos[6.66667*10^-12 omega] - 1. Cos[1.33333*10^-11 omega], 4. Sin[6.66667*10^-12 omega] + 1. Sin[1.33333*10^-11 omega]]

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  • $\begingroup$ Thanks! It works :) $\endgroup$
    – Jan SE
    Dec 1, 2017 at 11:47

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