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The Python cmath.acosh() function returns the complex inverse hyperbolic cosine of a complex number z. It is a function on complex plane, and has one branch cut, extending left from 1 along the real axis to -∞, continuous from above.

Mathematically, it can be expressed as:

complex acosh




z Required. Specify the value.

Return Value

Returns the complex inverse hyperbolic cosine of z.


In the example below, acosh() function is used to find out the complex inverse hyperbolic cosine of a given complex number.

import cmath

z1 = 2 + 2j
z2 = 2
z3 = 2j

print("cmath.acosh(z1):", cmath.acosh(z1))
print("cmath.acosh(z2):", cmath.acosh(z2))
print("cmath.acosh(z3):", cmath.acosh(z3))

The output of the above code will be:

cmath.acosh(z1): (1.7343245214879666+0.8165471820968505j)
cmath.acosh(z2): (1.3169578969248166+0j)
cmath.acosh(z3): (1.4436354751788103+1.5707963267948966j)

❮ Python cMath Module