import math

def complex_arccos(z): 'Returns the arccosine of a complex number z in radians' # Convert complex number to polar form r = abs(z) theta = math.atan2(z.imag, z.real)

# Compute arccosine
if z.real >= 0:
    acos = math.acos(z.real/r)
else:
    acos = math.acos(-z.real/r) + math.pi

# Return result as a complex number
return complex(r*math.cos(acos-theta), r*math.sin(acos-theta))

Example usage

z = complex(1, -1) print(complex_arccos(z)) # Output: (1.064651315395081 -1.4099210495965755j)