try google with 'complex acos' ???... lot of links to complex capable code and library for more or less all type of computer language.
from:
**broken link removed**
Code:
For input of a complex number, Z = X + iY, the complex arccosine is given by,
acos(Z) = acos(B) - i alog(A + sqrt(A^2 - 1)) if Y >= 0
acos(Z) = acos(B) + i alog(A + sqrt(A^2 - 1)) if Y < 0
where
A = 0.5 sqrt((X + 1)^2 + Y^2) + 0.5 sqrt((X - 1)^2 + Y^2)
B = 0.5 sqrt((X + 1)^2 + Y^2) - 0.5 sqrt((X - 1)^2 + Y^2)
seem not so hard to implement with real float math lib.
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for looking projekt with 'real life' using complex math. look a free42-project