mathjs/docs/complex_numbers.md

Complex

Math.js supports creation, manipulation, and calculations with complex numbers.

In mathematics, a complex number is an expression of the form a + bi, where a and b are real numbers, and i represents the imaginary number defined as i^2 = -1. (In other words, i is the square root of -1.) The real number a is called the real part of the complex number, and the real number b is the imaginary part. For example, 3 + 2i is a complex number, having real part 3 and imaginary part 2. Complex numbers are often used in applied mathematics, control theory, signal analysis, fluid dynamics and other fields.

API

A complex number is created using the function math.complex. This function accepts two numbers representing the real and imaginary part of the value, or a single string containing a complex value in the form a + bi where a and b respectively represent the real and imaginary part of the complex number. The function returns a Complex object.

Syntax:

math.complex(re: number) : Complex
math.complex(re: number, im: number) : Complex
math.complex(complex: Complex) : Complex
math.complex(str: string) : Complex

Examples:

var a = math.complex(2, 3);     // Complex 2 + 3i
a.re;                           // Number 2
a.im;                           // Number 3

var b = math.complex('4 - 2i'); // Complex 4 - 2i
b.re = 5;                       // Number 5
b;                              // Complex 5 - 2i

A Complex object has the following properties:

• re. A number containing the real part of the complex number.
• im. A number containing the imaginary part of the complex number.

The properties re and im of a complex number can be read and replaced.

A Complex object has the following functions:

• clone(). Create a clone of the complex number.
• equals(other). Test whether a complex number equals an other complex value. Two complex numbers are equal when both their real and imaginary parts are equal.
• toString(). Returns a string representation of the complex number, formatted as a + bi where a is the real part and b the imaginary part. The values are rounded to a fixed precision. The precision is defined in the option math.option.precision.

Calculations

Most functions of math.js support complex numbers. Complex and real numbers can be used together.

var a = math.complex(2, 3);     // Complex 2 + 3i
var b = math.complex('4 - 2i'); // Complex 4 - 2i

math.re(a);                     // Number 2
math.im(a);                     // Number 3
math.conj(a);                   // Complex 2 - 3i

math.add(a, b);                 // Complex 6 + i
math.multiply(a, 2);            // Complex 4 + 6i
math.sqrt(-4);                  // Complex 2i