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The cmath Module

The cmath module in Python provides mathematical functions for complex numbers. Unlike the standard math module, which only supports real numbers, cmath includes functions to handle complex numbers and their operations.

Importing the cmath Module

To use the functions from the cmath module, you need to import it into your Python script.

Python

import cmath

# Example usage
z = cmath.sqrt(-1)
print(z)  # Output: 1j

The above code demonstrates how to import the cmath module and use the sqrt function to compute the square root of a negative number, which results in a complex number.

Complex Number Creation

Complex numbers can be created using the complex() function or by directly using the j notation.

Python

# Using complex() function
z1 = complex(2, 3)  # 2 + 3j

# Using j notation
z2 = 4 + 5j

print(z1)  # Output: (2+3j)
print(z2)  # Output: (4+5j)

The complex() function takes two arguments, the real and imaginary parts of the complex number. Alternatively, you can directly use the j suffix to denote the imaginary part.

Mathematical Functions

The cmath module provides various mathematical functions specifically for complex numbers:

cmath.phase(z): Returns the phase of the complex number z.
cmath.polar(z): Returns the polar coordinates of the complex number z.
cmath.rect(r, phi): Converts polar coordinates (r, phi) to rectangular coordinates.
cmath.exp(z): Returns e raised to the power of the complex number z.
cmath.log(z): Returns the natural logarithm of the complex number z.
cmath.sqrt(z): Returns the square root of the complex number z.

Examples

Here are some examples of using these functions:

Python

import cmath

# Define a complex number
z = 3 + 4j

# Calculate phase
phase = cmath.phase(z)
print("Phase:", phase)  # Output: Phase: 0.9272952180016122

# Calculate polar coordinates
polar = cmath.polar(z)
print("Polar coordinates:", polar)  # Output: Polar coordinates: (5.0, 0.9272952180016122)

# Convert polar coordinates to rectangular
rect = cmath.rect(5, 0.9272952180016122)
print("Rectangular coordinates:", rect)  # Output: Rectangular coordinates: (3+4j)

# Calculate exponential
exp = cmath.exp(z)
print("Exponential:", exp)  # Output: Exponential: (-13.12878381524767-15.200784463067558j)

# Calculate logarithm
log = cmath.log(z)
print("Logarithm:", log)  # Output: Logarithm: (1.6094379124341003+0.9272952180016122j)

# Calculate square root
sqrt = cmath.sqrt(z)
print("Square root:", sqrt)  # Output: Square root: (2+1j)

These examples demonstrate how to compute various properties and transformations of complex numbers using the cmath module functions.

The cmath Module

Python mein cmath module complex numbers ke liye mathematical functions provide karta hai. Jabki standard math module sirf real numbers ko support karta hai, cmath module complex numbers aur unke operations ko handle karne ke liye functions include karta hai.

Import karna cmath Module

Agar aapko cmath module ke functions apne Python script mein use karne hain, to aapko pehle isko import karna padega.

Python

import cmath

# Example usage
z = cmath.sqrt(-1)
print(z)  # Output: 1j

Upar wale code mein dikhaya gaya hai ki kaise aap cmath module ko import karte hain aur sqrt function ka use karke ek negative number ka square root calculate karte hain, jo ki ek complex number return karta hai.

Complex Number Banana

Complex numbers aap complex() function ka use karke ya directly j notation ke through create kar sakte hain.

Python

# Using complex() function
z1 = complex(2, 3)  # 2 + 3j

# Using j notation
z2 = 4 + 5j

print(z1)  # Output: (2+3j)
print(z2)  # Output: (4+5j)

complex() function do arguments leta hai, real aur imaginary parts of the complex number. Alternatively, aap directly j suffix use kar ke imaginary part ko denote kar sakte hain.

Mathematical Functions

cmath module complex numbers ke liye kai mathematical functions provide karta hai:

cmath.phase(z): Complex number z ka phase return karta hai.
cmath.polar(z): Complex number z ke polar coordinates return karta hai.
cmath.rect(r, phi): Polar coordinates (r, phi) ko rectangular coordinates mein convert karta hai.
cmath.exp(z): Complex number z ke power mein e ko raise karta hai.
cmath.log(z): Complex number z ka natural logarithm return karta hai.
cmath.sqrt(z): Complex number z ka square root return karta hai.

Examples

Yahan kuch examples diye gaye hain in functions ka use karte hue:

Python

import cmath

# Define ek complex number
z = 3 + 4j

# Phase calculate karo
phase = cmath.phase(z)
print("Phase:", phase)  # Output: Phase: 0.9272952180016122

# Polar coordinates calculate karo
polar = cmath.polar(z)
print("Polar coordinates:", polar)  # Output: Polar coordinates: (5.0, 0.9272952180016122)

# Polar coordinates ko rectangular mein convert karo
rect = cmath.rect(5, 0.9272952180016122)
print("Rectangular coordinates:", rect)  # Output: Rectangular coordinates: (3+4j)

# Exponential calculate karo
exp = cmath.exp(z)
print("Exponential:", exp)  # Output: Exponential: (-13.12878381524767-15.200784463067558j)

# Logarithm calculate karo
log = cmath.log(z)
print("Logarithm:", log)  # Output: Logarithm: (1.6094379124341003+0.9272952180016122j)

# Square root calculate karo
sqrt = cmath.sqrt(z)
print("Square root:", sqrt)  # Output: Square root: (2+1j)

Ye examples dikhate hain ki kaise aap complex numbers ke properties aur transformations calculate kar sakte hain cmath module ke functions ka use karte hue.

Python Topics

The cmath Module

Importing the cmath Module

Complex Number Creation

Mathematical Functions

Examples

The cmath Module

Import karna cmath Module

Complex Number Banana

Mathematical Functions

Examples