**arccos(z)** is equal to

**− i × ln(z + √(z² − 1))** since

**cos(φ) = cosh(i × φ)**.

The arccosine is

real for -1 ≤ x ≤ 1 only. Values are then between 0 and

π. (I had originally written

defined instead of real, thanks to

IWhoSawTheFace for pointing out this ridiculous error to me)