Python cmath.atanh() Method with Examples

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cmath.atanh() Method in Python:

The cmath.atanh() method returns the complex number’s inverse hyperbolic tangent.

There are two types of branch cuts:

  1. Extends along the real axis from 1 to ∞, and is continuous from below.
  2. Extends along the real axis from -1 to -∞, and is continuous from above.

Syntax:

cmath.atanh(x)

Parameters

x: This is Required. It is a number used to calculate the inverse hyperbolic arctangent of

Return Value:

Returns a complex value that represents the complex number’s inverse hyperbolic tangent.

Examples:

Example1:

Input:

Given Complex Number = 3-4j

Output:

The given complex number's (3-4j) inverse hyperbolic tangent value = 
(0.1175009073114339-1.4099210495965755j)

Example2:

Input:

Given realpart = 5
Given imaginary part = 3

Output:

The given complex number's (5+3j) inverse hyperbolic tangent value = 
(0.14694666622552977+1.4808695768986575j)

Note: The above input format is for dynamic input.

cmath.atanh() Method with Examples in Python

Method #1: Using Built-in Functions (Static Input)

Approach:

  • Import cmath module(for complex number operations) using the import keyword.
  • Give the complex number as static input and store it in a variable.
  • Pass the given complex number as an argument to the cmath.atanh() method that returns the given complex number’s inverse hyperbolic tangent value.
  • Store it in another variable.
  • Print the inverse hyperbolic tangent value of the given complex number.
  • The Exit of the Program.

Below is the implementation:

# Import cmath module(for complex number operations) using the import keyword.
import cmath
# Give the complex number as static input and store it in a variable.
complexnumb = 3-4j
# Pass the given complex number as an argument to the cmath.atanh() method that
# returns the given complex number's inverse hyperbolic tangent value.
# Store it in another variable.
rslt = cmath.atanh(complexnumb)
# Print the inverse hyperbolic tangent value of the given complex number.
print("The given complex number's", complexnumb,
      "inverse hyperbolic tangent value = ")
print(rslt)

Output:

The given complex number's (3-4j) inverse hyperbolic tangent value = 
(0.1175009073114339-1.4099210495965755j)

Method #2: Using Built-in Functions (User Input)

Approach:

  • Import cmath module(for complex number operations) using the import keyword.
  • Give the real part and imaginary part of the complex number as user input using map(), int(), split().
  • Store it in two variables.
  • Using a complex() function convert those two variables into a complex number and store it in a variable.
  • Pass the given complex number as an argument to the cmath.atanh() method that returns the given complex number’s inverse hyperbolic tangent value.
  • Store it in another variable.
  • Print the inverse hyperbolic tangent value of the given complex number.
  • The Exit of the Program.

Below is the implementation:

# Import cmath module(for complex number operations) using the import keyword.
import cmath
# Give the real part and imaginary part of the complex number as user input
# using map(), int(), split().
# Store it in two variables.
realnumb, imaginarynumb = map(int, input(
    'Enter real part and complex part of the complex number = ').split())
# Using a complex() function convert those two variables into a complex number.
complexnumb = complex(realnumb, imaginarynumb)

# Pass the given complex number as an argument to the cmath.atanh() method that
# returns the given complex number's inverse hyperbolic tangent value.
# Store it in another variable.
rslt = cmath.atanh(complexnumb)
# Print the inverse hyperbolic tangent value of the given complex number.
print("The given complex number's", complexnumb,
      "inverse hyperbolic tangent value = ")
print(rslt)

Output:

Enter real part and complex part of the complex number = 5 3
The given complex number's (5+3j) inverse hyperbolic tangent value = 
(0.14694666622552977+1.4808695768986575j)