mathjs/examples/complex_numbers.js

// complex numbers

// load math.js (using node.js)
var math = require('../index');

// create a complex number with a numeric real and complex part
console.log('create and manipulate complex numbers');
var a = math.complex(2, 3);
print(a);                       // 2 + 3i

// read the real and complex parts of the complex number
print(a.re);                    // 2
print(a.im);                    // 3

// clone a complex value
var clone = a.clone();
print(clone);                   // 2 + 3i

// adjust the complex value
a.re = 5;
print(a);                       // 5 + 3i

// create a complex number by providing a string with real and complex parts
var b = math.complex('3-7i');
print(b);                       // 3 - 7i
console.log();

// perform operations with complex numbers
console.log('perform operations');
print(math.add(a, b));          // 8 - 4i
print(math.multiply(a, b));     // 36 - 26i
print(math.sin(a));             // -9.6541254768548 + 2.8416922956064i

// some operations will return a complex number depending on the arguments
print(math.sqrt(4));           // 2
print(math.sqrt(-4));          // 2i

// create a complex number from polar coordinates
console.log('create complex numbers with polar coordinates');
var c = math.complex({r: math.sqrt(2), phi: math.pi / 4});
print(c);                      // 1 + i

// get polar coordinates of a complex number
var d = math.complex(3, 4);
console.log(d.abs(), d.arg());      // radius = 5, phi = 0.9272952180016122

// comparision operations
// note that there is no mathematical ordering defined for complex numbers
// we can only check equality. To sort a list with complex numbers,
// the natural sorting can be used
console.log('\ncomparision and sorting operations');
console.log('equal', math.equal(a, b)); // returns false
var values = [a, b, c];
console.log('values:', math.format(values, 14)); // [5 + 3i, 3 - 7i, 1 + i]
math.sort(values, 'natural');
console.log('sorted:', math.format(values, 14)); // [1 + i, 3 - 7i, 5 + 3i]

/**
 * Helper function to output a value in the console. Value will be formatted.
 * @param {*} value
 */
function print (value) {
  var precision = 14;
  console.log(math.format(value, precision));
}