I'm trying to get the norm of a complex function with symbolic notation. But really I'm very inexperienced at this.
FullSimplify[Abs[ExpToTrig[Exp[I*x*t]]], Assumptions -> {t ∈ Reals, x ∈ Reals}]
With this code, I got 1. That's right!
So, now I'm trying to use this in the following problem: $\frac{e^{it(w_{21}+w)}-1}{w+w_{21}}+\frac{e^{it(w_{21}-w)}-1}{w_{21}-w}$
F[w_, t_] = Exp[I*w*t];
FullSimplify[
Abs[
ExpToTrig[
(F[w + Subscript[w, 21], t] - 1)/(w + Subscript[w, 21]) +
(F[Subscript[w, 21] - w, t] - 1)/(Subscript[w, 21] - w)]],
Assumptions -> {t ∈ Reals,Subscript[w, 21] ∈ Reals, w ∈ Reals}]
But in this case the function Abs
doesn't work. Can you tell me where I made my mistakes?
F[]
? $\endgroup$Abs[Exp[I*x*t]] // ComplexExpand
which as expected evaluates to1
$\endgroup$