{"maintainers":[{"name":"dev","email":"robert@raw.org"}],"keywords":["complex numbers","math","complex","number","calculus","parser","arithmetic"],"dist-tags":{"latest":"2.4.3"},"author":{"name":"Robert Eisele","email":"robert@raw.org","url":"https://raw.org/"},"description":"The RAW complex numbers library","readme":"# Complex.js - ℂ in JavaScript\n\n[![NPM Package](https://img.shields.io/npm/v/complex.js.svg?style=flat)](https://npmjs.org/package/complex.js \"View this project on npm\")\n[![MIT license](http://img.shields.io/badge/license-MIT-brightgreen.svg)](http://opensource.org/licenses/MIT)\n\nComplex.js is a well tested JavaScript library to work with [complex number arithmetic](https://raw.org/book/analysis/complex-numbers/) in JavaScript. It implements every elementary complex number manipulation function and the API is intentionally similar to [Fraction.js](https://github.com/rawify/Fraction.js). Furthermore, it's the basis of [Polynomial.js](https://github.com/rawify/Polynomial.js) and [Math.js](https://github.com/josdejong/mathjs).\n\n\n## Examples\n\n\n```js\nlet Complex = require('complex.js');\n\nlet c = new Complex(\"99.3+8i\");\nc.mul({re: 3, im: 9}).div(4.9).sub(3, 2);\n```\n\nA classical use case for complex numbers is solving quadratic equations `ax² + bx + c = 0` for all `a, b, c ∈ ℝ`:\n\n```js\n\nfunction quadraticRoot(a, b, c) {\n let sqrt = Complex(b * b - 4 * a * c).sqrt()\n let x1 = Complex(-b).add(sqrt).div(2 * a)\n let x2 = Complex(-b).sub(sqrt).div(2 * a)\n return {x1, x2}\n}\n\n// quadraticRoot(1, 4, 5) -> -2 ± i\n```\n\nFor cubic roots have a look at [RootFinder](https://github.com/rawify/RootFinder.js) which uses Complex.js.\n\n## Parser\n\n\nAny function (see below) as well as the constructor of the *Complex* class parses its input like this.\n\nYou can pass either Objects, Doubles or Strings.\n\n### Objects\n\n```javascript\nnew Complex({re: real, im: imaginary});\nnew Complex({arg: angle, abs: radius});\nnew Complex({phi: angle, r: radius});\nnew Complex([real, imaginary]); // Vector/Array syntax\n```\nIf there are other attributes on the passed object, they're not getting preserved and have to be merged manually.\n\n**Note:** Object attributes have to be of type Number to avoid undefined behavior.\n\n### Doubles\n\n```javascript\nnew Complex(55.4);\n```\n\n### Strings\n\n```javascript\nnew Complex(\"123.45\");\nnew Complex(\"15+3i\");\nnew Complex(\"i\");\n```\n\n### Two arguments\n\n```javascript\nnew Complex(3, 2); // 3+2i\n```\n\n## Attributes\n\n\nEvery complex number object exposes its real and imaginary part as attribute `re` and `im`:\n\n```javascript\nlet c = new Complex(3, 2);\n\nconsole.log(\"Real part:\", c.re); // 3\nconsole.log(\"Imaginary part:\", c.im); // 2\n```\n\n## Functions\n\n\nComplex sign()\n---\nReturns the complex sign, defined as the complex number normalized by it's absolute value\n\nComplex add(n)\n---\nAdds another complex number\n\nComplex sub(n)\n---\nSubtracts another complex number\n\nComplex mul(n)\n---\nMultiplies the number with another complex number\n\nComplex div(n)\n---\nDivides the number by another complex number\n\nComplex pow(exp)\n---\nReturns the number raised to the complex exponent (Note: `Complex.ZERO.pow(0) = Complex.ONE` by convention)\n\nComplex sqrt()\n---\nReturns the complex square root of the number\n\nComplex exp(n)\n---\nReturns `e^n` with complex exponent `n`.\n\nComplex log()\n---\nReturns the natural logarithm (base `E`) of the actual complex number\n\n_Note:_ The logarithm to a different base can be calculated with `z.log().div(Math.log(base))`.\n\ndouble abs()\n---\nCalculates the magnitude of the complex number\n\ndouble arg()\n---\nCalculates the angle of the complex number\n\nComplex inverse()\n---\nCalculates the multiplicative inverse of the complex number (1 / z)\n\nComplex conjugate()\n---\nCalculates the conjugate of the complex number (multiplies the imaginary part with -1)\n\nComplex neg()\n---\nNegates the number (multiplies both the real and imaginary part with -1) in order to get the additive inverse\n\nComplex floor([places=0])\n---\nFloors the complex number parts towards zero\n\nComplex ceil([places=0])\n---\nCeils the complex number parts off zero\n\nComplex round([places=0])\n---\nRounds the complex number parts\n\nboolean equals(n)\n---\nChecks if both numbers are exactly the same, if both numbers are infinite they\nare considered **not** equal.\n\nboolean isNaN()\n---\nChecks if the given number is not a number\n\nboolean isFinite()\n---\nChecks if the given number is finite\n\nComplex clone()\n---\nReturns a new Complex instance with the same real and imaginary properties\n\nArray toVector()\n---\nReturns a Vector of the actual complex number with two components\n\nString toString()\n---\nReturns a string representation of the actual number. As of v1.9.0 the output is a bit more human readable\n\n```javascript\nnew Complex(1, 2).toString(); // 1 + 2i\nnew Complex(0, 1).toString(); // i\nnew Complex(9, 0).toString(); // 9\nnew Complex(1, 1).toString(); // 1 + i\n```\n\ndouble valueOf()\n---\nReturns the real part of the number if imaginary part is zero. Otherwise `null`\n\n\n## Trigonometric functions\n\nThe following trigonometric functions are defined on Complex.js:\n\n| Trig | Arcus | Hyperbolic | Area-Hyperbolic |\n|------|-------|------------|------------------|\n| sin() | asin() | sinh() | asinh() |\n| cos() | acos() | cosh() | acosh() |\n| tan() | atan() | tanh() | atanh() |\n| cot() | acot() | coth() | acoth() |\n| sec() | asec() | sech() | asech() |\n| csc() | acsc() | csch() | acsch() |\n\n**Notes on branches & ranges.** Inverse trig on ℂ needs a branch choice. For `acot` there are two real-axis conventions:\n\n* **(Chosen) Textbook range (0, π) on ℝ.**\n Gives familiar real values (`acot(1)=π/4`, `acot(0)=π/2`, `acot(-1)=3π/4`). With the principal complex branch this **necessarily causes a π jump across the negative real axis** (e.g., near `-1±i0` → `-π/4`, but on `-1` → `3π/4`).\n **We implement this with `atan2(1, x)`** to select the correct quadrant and handle `x=0`.\n\n* **Alternative range (−π/2, π/2] on ℝ.**\n Makes `acot(-1) = -π/4` and can avoid that specific jump **only if the entire complex branch is changed to match**. Using plain `atan(1/x)` silently adopts this convention, changes real outputs, is undefined at `x=0`, and still wouldn’t resolve the complex behavior without a broader policy change.\n\nWe therefore prefer predictable, textbook real values and robust quadrant handling—hence `atan2(1, x)`-accepting the implied branch cut on ℝ⁻ by design.\n\n\n## Geometric Equivalence\n\n\nComplex 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:\n\nNew vector\n---\n```js\nlet v1 = new Complex(1, 0);\nlet v2 = new Complex(1, 1);\n```\n\nScale vector\n---\n```js\nscale(v1, factor):= v1.mul(factor)\n```\n\nVector norm\n---\n```js\nnorm(v):= v.abs()\n```\n\nTranslate vector\n---\n```js\ntranslate(v1, v2):= v1.add(v2)\n```\n\nRotate vector around center\n---\n```js\nrotate(v, angle):= v.mul({abs: 1, arg: angle})\n```\n\nRotate vector around a point\n---\n```js\nrotate(v, p, angle):= v.sub(p).mul({abs: 1, arg: angle}).add(p)\n```\n\nDistance to another vector\n---\n```js\ndistance(v1, v2):= v1.sub(v2).abs()\n```\n\n## Constants\n\n\nComplex.ZERO\n---\nA complex zero value (south pole on the Riemann Sphere)\n\nComplex.ONE\n---\nA complex one instance\n\nComplex.INFINITY\n---\nA complex infinity value (north pole on the Riemann Sphere)\n\nComplex.NAN\n---\nA complex NaN value (not on the Riemann Sphere)\n\nComplex.I\n---\nAn imaginary number i instance\n\nComplex.PI\n---\nA complex PI instance\n\nComplex.E\n---\nA complex euler number instance\n\nComplex.EPSILON\n---\nA small epsilon value used for `equals()` comparison in order to circumvent double imprecision.\n\n\n## Installation\n\nYou can install `Complex.js` via npm:\n\n```bash\nnpm install complex.js\n```\n\nOr with yarn:\n\n```bash\nyarn add complex.js\n```\n\nAlternatively, download or clone the repository:\n\n```bash\ngit clone https://github.com/rawify/Complex.js\n```\n\n## Usage\n\nInclude the `complex.min.js` file in your project:\n\n```html\n\n\n```\n\nOr in a Node.js project:\n\n```javascript\nconst Complex = require('complex.js');\n```\n\nor \n\n```javascript\nimport Complex from 'complex.js';\n```\n\n\n## Coding Style\n\nAs 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.\n\n## Building the library\n\nAfter cloning the Git repository run:\n\n```\nnpm install\nnpm run build\n```\n\n## Run a test\n\nTesting the source against the shipped test suite is as easy as\n\n```\nnpm run test\n```\n\n## Copyright and Licensing\n\nCopyright (c) 2025, [Robert Eisele](https://raw.org/)\nLicensed under the MIT license.\n","repository":{"type":"git","url":"git+ssh://git@github.com/rawify/Complex.js.git"},"users":{"rreusser":true,"snowdream":true,"xieranmaya":true,"johnsmithcoder":true},"bugs":{"url":"https://github.com/rawify/Complex.js/issues"},"license":"MIT","versions":{"1.0.0":{"name":"complex.js","version":"1.0.0","keywords":["math","complex","number","calculus"],"author":{"name":"Robert 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