Python cmath.atan() Method with Examples

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cmath.atan() Method in Python:

The cmath.atan() method returns the complex number’s arc tangent.

There are primarily two types of branch cuts:

  1. Extend from 1j along the imaginary axis to ∞ j to the right.
  2. Extending from -1j to -∞ j to the left along the imaginary axis

Syntax:

cmath.atan(x)

Parameters

x: This is Required. A number used to calculate the arc tangent of

Return Value:

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

Examples:

Example1:

Input:

Given Complex Number = 3+4j

Output:

The given complex number's (3+4j) arc tangent value = 
(1.4483069952314644+0.15899719167999918j)

Example2:

Input:

Given realpart = 5
Given imaginary part = 2

Output:

The given complex number's (5+2j) arc tangent value = 
(1.399284356584545+0.06706599664866984j)

Note: The above input format is for dynamic input.

cmath.atan() 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.atan() method that returns the given complex number’s arc tangent value.
  • Store it in another variable.
  • Print the arc 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.atan() method that
# returns the the given complex number's arc tangent value.
# Store it in another variable.
rslt = cmath.atan(complexnumb)
# Print the arc tangent value of the given complex number.
print("The given complex number's", complexnumb,
      "arc tangent value = ")
print(rslt)

Output:

The given complex number's (3+4j) arc tangent value = 
(1.4483069952314644+0.15899719167999918j)

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.atan() method that returns the given complex number’s arc tangent value.
  • Store it in another variable.
  • Print the arc 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.atan() method that
# returns the the given complex number's arc tangent value.
# Store it in another variable.
rslt = cmath.atan(complexnumb)
# Print the arc tangent value of the given complex number.
print("The given complex number's", complexnumb,
      "arc tangent value = ")
print(rslt)

Output:

Enter real part and complex part of the complex number = 5 2
The given complex number's (5+2j) arc tangent value = 
(1.399284356584545+0.06706599664866984j)