Python cmath.rect() Method with Examples

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cmath.rect() Method in Python:

The cmath.rect() method converts polar coordinates to the complex number’s rectangular form. It generates a complex number that includes phase and modulus.

This method equals r * (math.cos(phi) + math.sin(phi)*1j).

The radius r is the vector’s length, and phi (phase angle) is the angle formed with the real axis.

Syntax:

cmath.rect(r, phi)

Parameters

r: This is Required. The modulus of a complex number is represented by this symbol.

phi: This is Required. It represents a complex number’s phase.

Return Value:

Returns a complex value that represents a complex number in its rectangular form.

Examples:

Example1:

Input:

Given modulus = 2.135667
Given phase = 6.1111116

Output:

The rectangular form of the complex number =  (2.104127071172476-0.3656812864341552j)

Example2:

Input:

Given modulus = 5
Given phase = 2

Output:

The rectangular form of the complex number =  (-2.080734182735712+4.546487134128409j)

cmath.rect() 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 modulus of a complex number (r) as static input and store it in a variable.
  • Give the phase of a complex number (phi) as static input and store it in another variable.
  • Pass the given modulus, phase of a complex number as the arguments to the cmath.rect() method which returns a complex value that represents the complex number in its rectangular form.
  • Store it in another variable.
  • Print a complex value that represents the complex number in its rectangular form.
  • The Exit of the Program.

Below is the implementation:

# Import cmath module(for complex number operations) using the import keyword.
import cmath
# Give the modulus of a complex number (r) as static input and store it in a variable.
gvn_moduls_val = 2.135667
# Give the phase of a complex number (phi) as static input and store it
# in another variable.
gvn_phasee_val = 6.1111116
# Pass the given modulus, phase of a complex number as the arguments to the
# cmath.rect() method which returns a complex value that represents the
# complex number in its rectangular form.
# Store it in another variable.
rslt = cmath.rect(gvn_moduls_val, gvn_phasee_val)
# Print a complex value that represents the complex number in its rectangular form.
print("The rectangular form of the complex number = ", rslt)

Output:

The rectangular form of the complex number =  (2.104127071172476-0.3656812864341552j)

Similarly, try for the other examples

import cmath
gvn_moduls_val = 5
gvn_phasee_val = 2
rslt = cmath.rect(gvn_moduls_val, gvn_phasee_val)
print("The rectangular form of the complex number = ", rslt)

Output:

The rectangular form of the complex number =  (-2.080734182735712+4.546487134128409j)

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

Approach:

  • Import cmath module(for complex number operations) using the import keyword.
  • Give the modulus of a complex number (r) as user input using the float(input()) function and store it in a variable.
  • Give the phase of a complex number (phi) as user input using the float(input()) function and store it in another variable.
  • Pass the given modulus, phase of a complex number as the arguments to the cmath.rect() method which returns a complex value that represents the complex number in its rectangular form.
  • Store it in another variable.
  • Print a complex value that represents the complex number in its rectangular form.
  • The Exit of the Program.

Below is the implementation:

# Import cmath module(for complex number operations) using the import keyword.
import cmath
# Give the modulus of a complex number (r) as user input using the float(input()) function
# and store it in a variable.
gvn_moduls_val = float(input("Enter some random number = "))
# Give the phase of a complex number (phi) as user input using the float(input()) function
# and store it in another variable.
gvn_phasee_val = float(input("Enter some random number = "))
# Pass the given modulus, phase of a complex number as the arguments to the
# cmath.rect() method which returns a complex value that represents the
# complex number in its rectangular form.
# Store it in another variable.
rslt = cmath.rect(gvn_moduls_val, gvn_phasee_val)
# Print a complex value that represents the complex number in its rectangular form.
print("The rectangular form of the complex number = ", rslt)

Output:

Enter some random number = 1.56
Enter some random number = 2.34546
The rectangular form of the complex number = (-1.0911821806705588+1.1148638699801174j)