.TH "Complex" 3 2024-05-31 OCamldoc "OCaml library"
.SH NAME
Complex \- Complex numbers.
.SH Module
Module   Complex
.SH Documentation
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Module
.BI "Complex"
 : 
.B sig end

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Complex numbers\&.
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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 
.ft B
float
.ft R
)\&.

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.I type t 
= {
 re : 
.B float
;
 im : 
.B float
;
 }

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The type of complex numbers\&.  
.ft B
re
.ft R
is the real part and 
.ft B
im
.ft R
the
imaginary part\&.

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.I val zero 
: 
.B t
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The complex number 
.ft B
0
.ft R
\&.

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.I val one 
: 
.B t
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The complex number 
.ft B
1
.ft R
\&.

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.I val i 
: 
.B t
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The complex number 
.ft B
i
.ft R
\&.

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.I val neg 
: 
.B t -> t
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Unary negation\&.

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.I val conj 
: 
.B t -> t
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Conjugate: given the complex 
.ft B
x + i\&.y
.ft R
, returns 
.ft B
x \- i\&.y
.ft R
\&.

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.I val add 
: 
.B t -> t -> t
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Addition

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.I val sub 
: 
.B t -> t -> t
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Subtraction

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.I val mul 
: 
.B t -> t -> t
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Multiplication

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.I val inv 
: 
.B t -> t
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Multiplicative inverse (
.ft B
1/z
.ft R
)\&.

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.I val div 
: 
.B t -> t -> t
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Division

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.I val sqrt 
: 
.B t -> t
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Square root\&.  The result 
.ft B
x + i\&.y
.ft R
is such that 
.ft B
x > 0
.ft R
or
.ft B
x = 0
.ft R
and 
.ft B
y >= 0
.ft R
\&.
This function has a discontinuity along the negative real axis\&.

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.I val norm2 
: 
.B t -> float
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Norm squared: given 
.ft B
x + i\&.y
.ft R
, returns 
.ft B
x^2 + y^2
.ft R
\&.

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.I val norm 
: 
.B t -> float
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Norm: given 
.ft B
x + i\&.y
.ft R
, returns 
.ft B
sqrt(x^2 + y^2)
.ft R
\&.

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.I val arg 
: 
.B t -> float
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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
.ft B
\-pi
.ft R
to 
.ft B
pi
.ft R
\&.  This function has a discontinuity along the
negative real axis\&.

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.I val polar 
: 
.B float -> float -> t
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.ft B
polar norm arg
.ft R
returns the complex having norm 
.ft B
norm
.ft R
and argument 
.ft B
arg
.ft R
\&.

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.I val exp 
: 
.B t -> t
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Exponentiation\&.  
.ft B
exp z
.ft R
returns 
.ft B
e
.ft R
to the 
.ft B
z
.ft R
power\&.

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.I val log 
: 
.B t -> t
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Natural logarithm (in base 
.ft B
e
.ft R
)\&.

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.I val pow 
: 
.B t -> t -> t
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Power function\&.  
.ft B
pow z1 z2
.ft R
returns 
.ft B
z1
.ft R
to the 
.ft B
z2
.ft R
power\&.

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