Complex.js is a well tested JavaScript library to work with complex number arithmetic in JavaScript. It implements every elementary complex number manipulation function and the API is intentionally similar to Fraction.js. Furthermore, it's the basis of Polynomial.js and Math.js.
let Complex = require('complex.js');
let c = new Complex("99.3+8i");
c.mul({re: 3, im: 9}).div(4.9).sub(3, 2);A classical use case for complex numbers is solving quadratic equations ax² + bx + c = 0 for all a, b, c ∈ ℝ:
function quadraticRoot(a, b, c) {
let sqrt = Complex(b * b - 4 * a * c).sqrt()
let x1 = Complex(-b).add(sqrt).div(2 * a)
let x2 = Complex(-b).sub(sqrt).div(2 * a)
return {x1, x2}
}
// quadraticRoot(1, 4, 5) -> -2 ± iFor cubic roots have a look at RootFinder which uses Complex.js.
Any function (see below) as well as the constructor of the Complex class parses its input like this.
You can pass either Objects, Doubles or Strings.
new Complex({re: real, im: imaginary});
new Complex({arg: angle, abs: radius});
new Complex({phi: angle, r: radius});
new Complex([real, imaginary]); // Vector/Array syntaxIf there are other attributes on the passed object, they're not getting preserved and have to be merged manually.
Note: Object attributes have to be of type Number to avoid undefined behavior.
new Complex(55.4);new Complex("123.45");
new Complex("15+3i");
new Complex("i");new Complex(3, 2); // 3+2iEvery complex number object exposes its real and imaginary part as attribute re and im:
let c = new Complex(3, 2);
console.log("Real part:", c.re); // 3
console.log("Imaginary part:", c.im); // 2Returns the complex sign, defined as the complex number normalized by it's absolute value
Adds another complex number
Subtracts another complex number
Multiplies the number with another complex number
Divides the number by another complex number
Returns the number raised to the complex exponent (Note: Complex.ZERO.pow(0) = Complex.ONE by convention)
Returns the complex square root of the number
Returns e^n with complex exponent n.
Returns the natural logarithm (base E) of the actual complex number
Note: The logarithm to a different base can be calculated with z.log().div(Math.log(base)).
Calculates the magnitude of the complex number
Calculates the angle of the complex number
Calculates the multiplicative inverse of the complex number (1 / z)
Calculates the conjugate of the complex number (multiplies the imaginary part with -1)
Negates the number (multiplies both the real and imaginary part with -1) in order to get the additive inverse
Floors the complex number parts towards zero
Ceils the complex number parts off zero
Rounds the complex number parts
Checks if both numbers are exactly the same, if both numbers are infinite they are considered not equal.
Checks if the given number is not a number
Checks if the given number is finite
Returns a new Complex instance with the same real and imaginary properties
Returns a Vector of the actual complex number with two components
Returns a string representation of the actual number. As of v1.9.0 the output is a bit more human readable
new Complex(1, 2).toString(); // 1 + 2i
new Complex(0, 1).toString(); // i
new Complex(9, 0).toString(); // 9
new Complex(1, 1).toString(); // 1 + iReturns the real part of the number if imaginary part is zero. Otherwise null
The following trigonometric functions are defined on Complex.js:
| Trig | Arcus | Hyperbolic | Area-Hyperbolic |
|---|---|---|---|
| sin() | asin() | sinh() | asinh() |
| cos() | acos() | cosh() | acosh() |
| tan() | atan() | tanh() | atanh() |
| cot() | acot() | coth() | acoth() |
| sec() | asec() | sech() | asech() |
| csc() | acsc() | csch() | acsch() |
Complex numbers can also be seen as a vector in the 2D space. Here is a simple overview of basic operations and how to implement them with complex.js:
let v1 = new Complex(1, 0);
let v2 = new Complex(1, 1);scale(v1, factor):= v1.mul(factor)norm(v):= v.abs()translate(v1, v2):= v1.add(v2)rotate(v, angle):= v.mul({abs: 1, arg: angle})rotate(v, p, angle):= v.sub(p).mul({abs: 1, arg: angle}).add(p)distance(v1, v2):= v1.sub(v2).abs()A complex zero value (south pole on the Riemann Sphere)
A complex one instance
A complex infinity value (north pole on the Riemann Sphere)
A complex NaN value (not on the Riemann Sphere)
An imaginary number i instance
A complex PI instance
A complex euler number instance
A small epsilon value used for equals() comparison in order to circumvent double imprecision.
Installing complex.js is as easy as cloning this repo or use one of the following command:
npm install complex.js<script src="complex.min.js"></script>
<script>
console.log(Complex("4+3i"));
</script>As every library I publish, Complex.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library.
After cloning the Git repository run:
npm install
npm run build
Testing the source against the shipped test suite is as easy as
npm run test
Copyright (c) 2024, Robert Eisele Licensed under the MIT license.