module Complex:Complex numbers.`sig`

..`end`

This module provides arithmetic operations on complex numbers.
Complex numbers are represented by their real and imaginary parts
(cartesian representation). Each part is represented by a
double-precision floating-point number (type `float`

).

`type `

t = {

` ` |
`re : ` |

` ` |
`im : ` |

The type of complex numbers.

`re`

is the real part and `im`

the
imaginary part.`val zero : ``t`

The complex number

`0`

.`val one : ``t`

The complex number

`1`

.`val i : ``t`

The complex number

`i`

.`val neg : ``t -> t`

Unary negation.

`val conj : ``t -> t`

Conjugate: given the complex

`x + i.y`

, returns `x - i.y`

.`val add : ``t -> t -> t`

Addition

`val sub : ``t -> t -> t`

Subtraction

`val mul : ``t -> t -> t`

Multiplication

`val inv : ``t -> t`

Multiplicative inverse (

`1/z`

).`val div : ``t -> t -> t`

Division

`val sqrt : ``t -> t`

Square root. The result

`x + i.y`

is such that `x > 0`

or
`x = 0`

and `y >= 0`

.
This function has a discontinuity along the negative real axis.`val norm2 : ``t -> float`

Norm squared: given

`x + i.y`

, returns `x^2 + y^2`

.`val norm : ``t -> float`

Norm: given

`x + i.y`

, returns `sqrt(x^2 + y^2)`

.`val arg : ``t -> float`

Argument. The argument of a complex number is the angle
in the complex plane between the positive real axis and a line
passing through zero and the number. This angle ranges from

`-pi`

to `pi`

. This function has a discontinuity along the
negative real axis.`val polar : ``float -> float -> t`

`polar norm arg`

returns the complex having norm `norm`

and argument `arg`

.`val exp : ``t -> t`

Exponentiation.

`exp z`

returns `e`

to the `z`

power.`val log : ``t -> t`

Natural logarithm (in base

`e`

).`val pow : ``t -> t -> t`

Power function.

`pow z1 z2`

returns `z1`

to the `z2`

power.