Python cmath.phase Function

The cmath.rect function in Python's cmath module returns the complex number corresponding to the given polar coordinates. It takes a modulus (radius) and a phase (angle) and converts them into a complex number in rectangular form. This function is useful in various fields, including electrical engineering, signal processing, and complex analysis.

Table of Contents

  1. Introduction
  2. cmath.rect Function Syntax
  3. Examples
    • Basic Usage
    • Converting Polar Coordinates to Rectangular Form
  4. Real-World Use Case
  5. Conclusion

Introduction

The cmath.rect function converts polar coordinates to a complex number in rectangular form. The function is essential for working with polar representations of complex numbers, which are common in various engineering and scientific applications.

cmath.rect Function Syntax

Here is how you use the cmath.rect function:

import cmath

result = cmath.rect(r, phi)

Parameters:

  • r: The modulus (radius) of the complex number.
  • phi: The phase (angle) of the complex number in radians.

Returns:

  • A complex number corresponding to the given polar coordinates.

Examples

Basic Usage

Convert polar coordinates to a complex number.

Example

import cmath

r = 2
phi = cmath.pi / 4
result = cmath.rect(r, phi)
print(f"rect({r}, {phi}) = {result}")

Output:

rect(2, 0.7853981633974483) = (1.4142135623730951+1.4142135623730951j)

Converting Polar Coordinates to Rectangular Form

Convert another set of polar coordinates to a complex number.

Example

import cmath

r = 1
phi = cmath.pi / 2
result = cmath.rect(r, phi)
print(f"rect({r}, {phi}) = {result}")

Output:

rect(1, 1.5707963267948966) = (6.123233995736766e-17+1j)

Real-World Use Case

Signal Processing

In signal processing, you may need to convert polar coordinates of a signal to rectangular form. The cmath.rect function can be used to determine this.

Example

import cmath

# Example polar coordinates of a signal
modulus = 2
phase = cmath.pi / 3
rectangular_form = cmath.rect(modulus, phase)

print(f"The rectangular form of the signal with modulus {modulus} and phase {phase} radians is {rectangular_form}")

Output:

The rectangular form of the signal with modulus 2 and phase 1.0471975511965976 radians is (1.0000000000000002+1.7320508075688772j)

Conclusion

The cmath.rect function is used for converting polar coordinates to complex numbers in rectangular form in Python. It returns a complex number corresponding to the given modulus and phase, which is useful in various fields, such as signal processing and electrical engineering. By understanding how to use this function, you can effectively work with polar and rectangular representations of complex numbers.

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