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Math.js: Complex Numbers

JS Calc provides comprehensive support for complex numbers through Math.js, allowing for arithmetic and the use of complex numbers with many standard mathematical functions.

Creating Complex Numbers

  1. Direct Input (using i): The imaginary unit i (representing sqrt(-1)) is a built-in constant.
> 2 + 3i
 2 + 3i

> 5i
 5i

> -2.5 - 1.8i
 -2.5 - 1.8i

  1. Using the complex() function:

    Syntax: complex(realPart, imaginaryPart) or complex(polarFormString)

> complex(4, -2)
 4 - 2i

> complex("3 + 4i")
 3 + 4i

> complex({r: 5, phi: pi/4}) // Polar form: radius 5, angle pi/4
 3.5355339059327378 + 3.535533905932737i

Operations with Complex Numbers

Most standard arithmetic operators and mathematical functions work seamlessly with complex numbers.

Arithmetic

> z1 = 1 + 2i
> z2 = 3 - 4i
> z1 + z2
 4 - 2i

> z1 * z2
 11 + 2i

> (2+i) / (1-i)
 0.5 + 1.5i

> (1+i)^3
 -2 + 2i

Common Functions

  • re(z): Real part of z.
> re(3 + 7i)
 3
  • im(z): Imaginary part of z.
> im(3 + 7i)
 7
  • conj(z): Complex conjugate of z.
> conj(3 + 7i)
 3 - 7i
  • abs(z): Absolute value (magnitude or modulus) of z.
> abs(3 + 4i)  // sqrt(3^2 + 4^2)
 5
  • arg(z): Argument (angle or phase) of z in radians.
> arg(1 + i) // atan2(1,1)
 0.7853981633974483 (pi/4)
  • sqrt(z): Square root.
> sqrt(-4)
 2i
> sqrt(2i)
 1 + i
  • exp(z), log(z), sin(z), cos(z), etc., all support complex arguments.
> exp(i*pi) // Euler's Identity
 -1

> log(-1)
 3.141592653589793i // i*pi

Persistence

Complex numbers assigned to variables are saved and persist between sessions.

For more details, refer to the Math.js Complex Numbers Documentation.