# functional analysis – simple question about and unitary element and self-adjointness

In Murphy’s book P42, it says

If $$A$$ is a unital $$C^*$$– algebra and $$a$$ is self-adjoint in $$A$$, then $$e^{ia}$$ is unitary.

Why is the statement true?

I’ve been playing around with the involution. But I don’t see how we get $$(e^{ia})^* = e^{-ia}$$.

Thank you for your help!