Complex conjugate of an involved expression I understand the the complex conjugate of, say, $z:=\exp({a+ib})$ is $z:=\exp({a-ib})$.
However , I have a composite expression  and I'm not sure how to attack taking it's complex conjugate.
Say $z:=i\exp({ib}) / ({a + ic})$
I would be tempted to say that the denominator becomes ${a - ic}$, that the denominator changes signs & the exponential as well, so:
$z*:=-i\exp({-ib}) / ({a - ic})$
I'm asking because I need to compute the norm of a complex expression (which structurally is similar to this exemple) and I feel I'm about to embark on a rather lengthy derivation, based in part on the computation of that norm... hence would like to know if my understanding of the complex conjugate is accurate in a more involved case.
Thanks
EDIT: wrt to comment: a, b, and c are real (e.g. I have explicited any imaginary part)

If $z=e^{a+ib}$ then $z=e^a(\cos b+i\sin b)$, so $\bar z=e^a(\cos b-i\sin b)$ and then $\bar z=e^{a-ib}$.
