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Works seamlessly in browsers and Node.js.","maintainers":[{"name":"squaremarco","email":"sq@iamsquare.it"}],"readme":"![Logo](https://raw.githubusercontent.com/iamsquare/complex.js/master/logo.png)\n\n# [ℂomplex.js](https://complex-js.iamsquare.it)\n\n[![NPM](https://img.shields.io/npm/v/@iamsquare/complex.js.svg?style=flat-square)](https://www.npmjs.com/package/@iamsquare/complex.js)\n[![GitHub issues](https://img.shields.io/github/issues-raw/iamsquare/complex.js.svg?style=flat-square)](https://github.com/iamsquare/complex.js/issues)\n[![GitHub License](https://img.shields.io/github/license/mashape/apistatus.svg?style=flat-square)](https://github.com/iamsquare/complex.js/blob/master/LICENSE)\n[![NPM](https://nodei.co/npm/@iamsquare/complex.js.png?mini=true)](https://nodei.co/npm/@iamsquare/complex.js)\n\n> A powerful, type-safe complex numbers library for JavaScript and TypeScript. Works seamlessly in browsers and Node.js.\n\n**Complex.js** provides a comprehensive set of operations and functions for complex number arithmetic, trigonometry, hyperbolic functions, and more. Built with TypeScript, it includes full type definitions out of the box.\n\n## Features\n\n- **Complete Complex Number Operations** - Addition, subtraction, multiplication, division, and more\n- **Trigonometric Functions** - sin, cos, tan, sec, csc, cot and their inverses\n- **Hyperbolic Functions** - sinh, cosh, tanh, sech, csch, coth and their inverses\n- **Mathematical Functions** - Exponentiation, logarithms, powers, square roots, principal values (n-th roots)\n- **Numerically Stable** - Uses robust floating-point comparisons (combining absolute and relative error) and stable algorithms to handle precision errors\n- **TypeScript Support** - Full type definitions included, no `@types` package needed\n- **Universal** - Works in both browsers and Node.js\n- **Zero Dependencies** - Lightweight and fast\n- **Multiple Representations** - Create from Cartesian, polar, or numeric coordinates\n\n## Installation\n\nInstall Complex.js using [npm](https://www.npmjs.com/package/@iamsquare/complex.js) or [pnpm](https://pnpm.io/):\n\n```bash\nnpm i @iamsquare/complex.js\n# or\npnpm i @iamsquare/complex.js\n```\n\n## Quick Start\n\n```typescript\nimport { Complex, add, sum, multiply, sin, exp } from '@iamsquare/complex.js';\n\n// Create complex numbers\nconst z = new Complex(1, -1);\nconst w = new Complex({ x: 1, y: -3 });\nconst k = new Complex({ r: 1, p: Math.PI / 2 });\n\n// Perform operations\nconst addition = add(z, w);\nconst total = sum(z, w, k);\nconst product = multiply(z, w);\nconst sine = sin(z);\nconst exponential = exp(z);\n\nconsole.log(addition.toString()); // => \"2 - 4i\"\n```\n\n## Usage\n\n### Creating Complex Numbers\n\nComplex numbers can be created in several ways:\n\n```typescript\n// Numeric arguments (real, imaginary)\nconst z = new Complex(1, -1);\n\n// Cartesian coordinates\nconst w = new Complex({ x: 1, y: -3 });\n\n// Polar coordinates (radius, phase in radians)\nconst k = new Complex({ r: 1, p: Math.PI / 2 });\n\n// From another Complex number\nconst zz = new Complex(z);\n```\n\n### Accessing Parts\n\n```typescript\nconst z = new Complex(3, 4);\n\n// Get real and imaginary parts\nconst realPart = z.getRe(); // 3\nconst imagPart = z.getIm(); // 4\n\n// Convert to different representations\nconst cartesian = z.toCartesian(); // { x: 3, y: 4 }\nconst polar = z.toPolar(); // { r: 5, p: 0.9272952180016122 }\n```\n\n### Basic Arithmetic Operations\n\n```typescript\nimport { Complex, add, sum, subtract, multiply, divide, negate } from '@iamsquare/complex.js';\n\nconst z = new Complex(1, -1);\nconst w = new Complex(1, -3);\n\n// Addition\nconst addition = add(z, w);\nconsole.log(addition.toString()); // => \"2 - 4i\"\n\n// Sum multiple numbers\nconst z1 = new Complex(1, 2);\nconst z2 = new Complex(3, 4);\nconst z3 = new Complex(5, 6);\nconst total = sum(z1, z2, z3);\nconsole.log(total.toString()); // => \"9 + 12i\"\n\n// Subtraction\nconst diff = subtract(z, w);\nconsole.log(diff.toString()); // => \"0 + 2i\"\n\n// Multiplication\nconst product = multiply(z, w);\nconsole.log(product.toString()); // => \"-2 - 4i\"\n\n// Division\nconst quotient = divide(z, w);\nconsole.log(quotient.toString()); // => \"0.4 + 0.2i\"\n\n// Negation\nconst negated = negate(z);\nconsole.log(negated.toString()); // => \"-1 + 1i\"\n```\n\n### Mathematical Functions\n\n```typescript\nimport {\n  Complex,\n  exp,\n  log,\n  pow,\n  sqrt,\n  principal,\n  sin,\n  cos,\n  tan,\n  sinh,\n  cosh,\n  tanh,\n  asin,\n  asinh,\n} from '@iamsquare/complex.js';\n\nconst z = new Complex(1, 1);\n\n// Exponential and logarithmic functions\nconst e = exp(z);\nconst ln = log(z);\nconst power = pow(z, new Complex(2, 0));\nconst root = sqrt(z);\nconst cubeRoot = principal(z, 3);\n\n// Trigonometric functions\nconst sine = sin(z);\nconst cosine = cos(z);\nconst tangent = tan(z);\n\n// Hyperbolic functions\nconst hypSine = sinh(z);\nconst hypCosine = cosh(z);\nconst hypTangent = tanh(z);\n\n// Inverse functions\nconst arcSine = asin(z);\nconst arcHyperSine = asinh(z);\n```\n\n### Utility Operations\n\n```typescript\nimport {\n  Complex,\n  modulus,\n  argument,\n  conjugate,\n  unit,\n  equals,\n  isApproximatelyEqual,\n  isReal,\n  isZero,\n} from '@iamsquare/complex.js';\n\nconst z = new Complex(3, 4);\n\n// Modulus (absolute value)\nconst mod = modulus(z); // 5\n\n// Argument (phase)\nconst arg = argument(z); // 0.9272952180016122\n\n// Complex conjugate\nconst conj = conjugate(z); // 3 - 4i\n\n// Unit vector\nconst unitVec = unit(z); // 0.6 + 0.8i\n\n// Equality checks (uses epsilon-based comparison for floating-point precision)\nconst isEqual = equals(z, new Complex(3, 4)); // true\nconst isRealNum = isReal(z); // false\nconst isZeroNum = isZero(z); // false\n\n// Compare floating-point numbers\nconst approxEqual = isApproximatelyEqual(0.1 + 0.2, 0.3); // true\n```\n\n### Predefined Constants\n\n```typescript\nComplex.ZERO; // 0\nComplex.ONE; // 1\nComplex.I; // i (imaginary unit)\nComplex.PI; // π\nComplex.HALFPI; // π/2\nComplex.E; // e (Euler's number)\nComplex.INFINITY; // ∞\nComplex.NAN; // NaN\nComplex.EPSILON; // Machine epsilon\n```\n\n## 📖 Documentation\n\nComprehensive documentation is available at **[https://complex-js.iamsquare.it](https://complex-js.iamsquare.it)**.\n\nThe documentation includes:\n\n- Complete API reference\n- Detailed examples\n- Mathematical background\n- Usage guides\n\n### Local Documentation Development\n\nThe documentation website is built using [Docusaurus](https://docusaurus.io/). To work with the documentation locally:\n\n```bash\ncd docusaurus\npnpm install\npnpm start\n```\n\nThis starts a local development server. Most changes are reflected live without restarting the server.\n\nTo build the documentation:\n\n```bash\ncd docusaurus\npnpm build\n```\n\n## Development\n\n### Building from Source\n\nClone the repository and build the library:\n\n```bash\ngit clone https://github.com/iamsquare/complex.js.git\ncd complex.js\npnpm install\npnpm run prod\n```\n\n`pnpm run prod` runs tests with coverage and builds the library only if all tests pass. To build without testing:\n\n```bash\npnpm run build\n```\n\n> **Note**: This project uses [pnpm](https://pnpm.io/) as its package manager. The `preinstall` script will enforce this.\n\n### Available Scripts\n\n- `pnpm test` - Run tests\n- `pnpm test:watch` - Run tests in watch mode\n- `pnpm test:coverage` - Run tests with coverage\n- `pnpm build` - Build the library\n- `pnpm lint` - Run ESLint\n- `pnpm lint:fix` - Fix ESLint issues\n- `pnpm prod` - Clean, test with coverage, and build\n\n## Contributing\n\nContributions are welcome! Please feel free to submit a Pull Request. For major changes, please open an issue first to discuss what you would like to change.\n\nPlease read our [Contributing Guide](.github/CONTRIBUTING.md) for details on our development process and how to submit pull requests.\n\n## License\n\nThis project is licensed under the [MIT License](LICENSE).\n\n## Built With\n\n- [TypeScript](https://www.typescriptlang.org/) - Main language\n- [Vitest](https://vitest.dev/) - Testing framework\n- [Rollup](https://rollupjs.org/) - Module bundler\n- [Docusaurus](https://docusaurus.io/) - Documentation website framework\n- [pnpm](https://pnpm.io/) - Fast, disk space efficient package manager\n\n---\n\nMade with ❤️ by [iamsquare](https://iamsquare.it)\n","readmeFilename":"README.md"}