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Additional and modified functions for complex numbers.

Complex numbers.

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 = Complex.t = {`
1. `re : float;`
2. `im : float;`
`}`
`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`

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

Subtraction

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

Multiplication

`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 operations : t BatNumber.numeric`
`val inv : t -> t`

`inv x` returns the value of `1/x`

`val succ : t -> t`

Add `one` to this number.

`val pred : t -> t`

Remove `one` from this number.

`val abs : t -> t`

`abs c` returns the module of this complex number, i.e. `abs c = Float.sqrt((re c) *. (re c) +. (im c) *. (im c) )`

`val modulo : t -> t -> t`
`val pow : t -> t -> t`
`val compare : t -> t -> int`
`val ord : t -> t -> BatOrd.order`
`val equal : t -> t -> bool`
`val of_int : int -> t`
`val to_int : t -> int`

`to_int c` is the integer part of the real part of `c`

`val of_string : string -> t`

`of_string s` accepts strings with the following formats:

(<int>|<float>) (+|-) i ( * | . | ) (<int>|<float>)

where (a|b|c) is either a or b or c.

In addition the following degenerate formats are also accepted:

(+|-) i ( * | . | ) (<int>|<float>)

(<int>|<float>) (+|-) i

(<int>|<float>)

`val to_string : t -> string`
`val (+) : t -> t -> t`
`val (-) : t -> t -> t`
`val (*) : t -> t -> t`
`val (/) : t -> t -> t`
`val (**) : t -> t -> t`
`val (--) : t -> t -> t BatEnum.t`
`val (---) : t -> t -> t BatEnum.t`
`val of_float : float -> t`

`Complex.of_float x` returns the complex number `x+0i`

`val to_float : t -> float`

`Complex.to_float (a+bi)` returns the float `a`

###### Submodules grouping all infix operators
`module Infix : BatNumber.Infix with type bat__infix_t = t`
`module Compare : BatNumber.Compare with type bat__compare_t = t`
###### Boilerplate code
`val print : 'a BatInnerIO.output -> t -> unit`

Printing