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The Python cmath.atanh() function returns the complex inverse hyperbolic tangent of a complex number z. It is a function on complex plane, and has two branch cuts:

  • Extends from 1 along the real axis to ∞, continuous from below.
  • Extends from -1 along the real axis to -∞, continuous from above.

Mathematically, it can be expressed as:

complex atanh

Syntax

cmath.atanh(z)

Parameters

z Required. Specify the value.

Return Value

Returns the complex inverse hyperbolic tangent of z.

Example:

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

import cmath

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

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

The output of the above code will be:

cmath.atanh(z1): (0.23887786125685911+1.311223269671635j)
cmath.atanh(z2): (0.5493061443340549+1.5707963267948966j)
cmath.atanh(z3): 1.1071487177940904j

❮ Python cMath Module