My question is about an apparent failure of the function "FullSimplify" to simplify an easy algebraic expression.
This is the expression that I ask Mathematica to evaluate:
FullSimplify[Re[a^(I*b)] - Re[a^(-I*b)], Element[a, Reals] && a > 0 && Element[b, Reals]]
This should give the result 0. Instead Mathematica only restates my expression:
Re[a^(-I b) (-1 + a^(2 I b))]
Replacing a and b by actual numbers solves the problem.
What could be the cause of it? How to effectively use FullSimplify (and Simplify, Expand, Integrate and so...) with assumptions?
I read that the order of variables could play a role here, but I couldn't wrap my head around it.
I tried to check for similar problems on the website as well, but I couldn't find any answer that could explain this phenomenon.
Thanks in advance for your support.