Complex Number Class 🔢

This class includes many trig functions and is immutable. None of its methods will change the real or imaginary components, instead, they return new complex objects.

To retrieve the real and imaginary parts of the complex number z, use z.real and z.imag.

Method Chaining 🔗

Most methods can be chained. For example, z.tan().sqrt() will calculate and return the square root of the tangent of z. In mathematics, we are evaluating sqrt(tan(z)) leaving z unchanged.

Floating Point Errors 🔍

In some situations, floating point errors can be significant. Testing for equality or to see if the number represents a real value can be problematic. By default, the maximum permitted difference is 10^-8; but in some situations, this may be too restrictive and reject values you wish to consider equal. Use accessor Complex.epsilon to change the static #epsilon property's default value.

⚠️ Notice that b/c Complex.epsilon is a static accessor, changing it affects all instances of class Complex. As a workaround, all methods which rely on it accept an optional epsilon argument to be used in the test, thus ignoring the global static default value.

Additional Information ℹ️

• Last updated: 16 Aug 2023

• Author: Peter Lager (2023)

• Refactored by GoToLoop (2023)

• Complex on GitHub

• Documentation

Complex

Summary

The code defines a class called Complex that represents complex numbers. It provides various mathematical operations and utility methods for working with complex numbers.

Example Usage

// Create a complex number
const z = new Complex(2, 3);

// Perform mathematical operations
const sum = z.add(new Complex(1, 1));
const product = z.mult(2);
const abs = z.abs();

// Print the complex number
console.log(z.toString());

Code Analysis

Main functionalities

• Represents complex numbers with real and imaginary parts
• Provides mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.
• Supports trigonometric and hyperbolic functions for complex numbers
• Allows conversion between polar and rectangular coordinates
• Provides methods for comparing complex numbers and finding roots

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Methods

• abs(): Calculates the absolute value (modulus) of the complex number
• add(n): Adds another complex number or a real number to the complex number
• acos(): Calculates the inverse cosine of the complex number
• arg(): Calculates the argument (phase) of the complex number in radians
• asin(): Calculates the inverse sine of the complex number
• atan(): Calculates the inverse tangent of the complex number
• cbrt(): Calculates the cube root of the complex number
• clone(): Creates a copy of the complex number
• conj(): Calculates the conjugate of the complex number
• cos(): Calculates the cosine of the complex number
• cosec(): Calculates the cosecant of the complex number
• cosech(): Calculates the hyperbolic cosecant of the complex number
• cosh(): Calculates the hyperbolic cosine of the complex number
• cot(): Calculates the cotangent of the complex number
• coth(): Calculates the hyperbolic cotangent of the complex number
• cubed(): Calculates the cube of the complex number
• div(n): Divides the complex number by another complex number or a scalar
• equals(z, epsilon): Checks if the complex number is equal to another complex number within a given tolerance
• exp(): Calculates the exponential of the complex number
• hashCode(hash): Generates a hashcode for the complex number
• isReal(epsilon): Checks if complex number is real within a given tolerance
• isZero(epsilon): Checks if complex number is zero within a given tolerance
• log(): Calculates the natural logarithm of the complex number
• mult(n): Multiplies the complex number by another complex number or a scalar
• negate(): Returns the negation of the complex number
• norm(): Returns the normalization of the complex number
• pow(n): Returns the complex number raised to a given exponent
• roots(n): Returns the nth roots of the complex number
• sin(): Calculates the sine of the complex number
• sinh(): Calculates the hyperbolic sine of the complex number
• squared(): Returns the square of the complex number
• sqrt(): Returns the square root of the complex number
• sub(n): Subtracts another complex number or real number from complex number
• tan(): Returns the tangent of the complex number
• tanh(): Returns the hyperbolic tangent of the complex number
• print(precision): Prints the complex number to the console
• $(precision, $): Returns a string representation of the complex number

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Fields

• real: The real part of the complex number
• imag: The imaginary part of the complex number
• #hashCode: The cached hashcode for the complex number
• #$: The cached string representation for the complex number

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