ACOS logarithmic form

[Claudio L.]

(04-30-2016 08:57 AM)ljubo Wrote:  ...it is interesting question why they have chosen this exact principal branch - or in other words, what would be broken or "ugly" if principal branch would be different, especially if they would took Im(ARCCOS(z))<0 for Re(z)>1 and Im(z)=0.

Thank you, now I don't feel so dumb. The first few posts seemed to dismiss this as something trivial that I should've known since third grade. I'm glad to see now that it wasn't so trivial.
Back on topic, it seems you are on the right track, I think those branches were chosen to preserve the symmetries and the relationships between asin() and acos() that we know from the real realm.
I guess all you have to do is get a list of all symmetries, and test them using the Wikipedia formula for acos().
I can easily see acos(Z)=pi/2-asin(Z) failing if you have the other branch, since the sign of the imaginary part is opposite, you'd get acos(Z)=pi/2-conj(asin(Z)).