Inheritance diagram for MathPHP\Number\Complex:

Collaboration diagram for MathPHP\Number\Complex:

Public Member Functions
	__construct ($r, $i)
	Constructor: __construct. More...

	__toString ()
	Function: __toString String representation of a complex number a + bi, a - bi, etc. More...

	__get (string $part)
	Function: __get Get r or i. More...

	complexConjugate ()
	The conjugate of a complex number. More...

	abs ()
	The absolute value (magnitude) of a complex number (modulus) https://en.wikipedia.org/wiki/Complex_number#Absolute_value_and_argument. More...

	arg ()
	The argument (phase) of a complex number The argument of z is the angle of the radius OP with the positive real axis, and is written as arg(z). More...

	sqrt ()
	The square root of a complex number https://en.wikipedia.org/wiki/Complex_number#Square_root. More...

	roots ()
	The roots of a complex number https://en.wikipedia.org/wiki/Complex_number#Square_root. More...

	inverse ()
	The inverse of a complex number (reciprocal) More...

	negate ()
	Negate the complex number Switches the signs of both the real and imaginary parts. More...

	polarForm ()
	Polar form https://en.wikipedia.org/wiki/Complex_number#Polar_form. More...

	add ($c)
	Complex addition https://en.wikipedia.org/wiki/Complex_number#Addition_and_subtraction. More...

	subtract ($c)
	Complex subtraction https://en.wikipedia.org/wiki/Complex_number#Addition_and_subtraction. More...

	multiply ($c)
	Complex multiplication https://en.wikipedia.org/wiki/Complex_number#Multiplication_and_division. More...

	divide ($c)
	Complex division Dividing two complex numbers is accomplished by multiplying the first by the inverse of the second https://en.wikipedia.org/wiki/Complex_number#Multiplication_and_division. More...

	equals (Complex $c)
	Test for equality Two complex numbers are equal if and only if both their real and imaginary parts are equal. More...

Public Attributes
const	EPSILON = 1e-6
	Floating-point range near zero to consider insignificant.

Protected Attributes
	$r

	$i

Detailed Description

Class: Complex Complex Numbers.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation i² = −1. In this expression, a is the real part and b is the imaginary part of the complex number. https://en.wikipedia.org/wiki/Complex_number

Constructor & Destructor Documentation

◆ __construct()

MathPHP\Number\Complex::__construct	(	$r,
		$i
	)

Constructor: __construct.

Parameters

number	$r	Real part
number	$i	Imaginary part

Member Function Documentation

◆ __get()

MathPHP\Number\Complex::__get ( string $part )

Function: __get Get r or i.

Parameters

string $part

Returns: number

Exceptions

Exception

◆ __toString()

MathPHP\Number\Complex::__toString ( )

Function: __toString String representation of a complex number a + bi, a - bi, etc.

Returns: string

◆ abs()

MathPHP\Number\Complex::abs ( )

The absolute value (magnitude) of a complex number (modulus) https://en.wikipedia.org/wiki/Complex_number#Absolute_value_and_argument.

If z = a + bi

|z| = √a² + b²

Returns: number

◆ add()

MathPHP\Number\Complex::add ( $c )

Complex addition https://en.wikipedia.org/wiki/Complex_number#Addition_and_subtraction.

(a + bi) + (c + di) = (a + c) + (b + d)i

Parameters

mixed $c

Returns: Complex

Exceptions

Exception

Implements MathPHP\Number\ObjectArithmetic.

◆ arg()

MathPHP\Number\Complex::arg ( )

The argument (phase) of a complex number The argument of z is the angle of the radius OP with the positive real axis, and is written as arg(z).

https://en.wikipedia.org/wiki/Complex_number#Absolute_value_and_argument

If z = a + bi arg(z) = atan(b, a)

Returns: number

◆ complexConjugate()

MathPHP\Number\Complex::complexConjugate ( )

The conjugate of a complex number.

https://en.wikipedia.org/wiki/Complex_number#Conjugate

Returns: Complex

◆ divide()

MathPHP\Number\Complex::divide ( $c )

Complex division Dividing two complex numbers is accomplished by multiplying the first by the inverse of the second https://en.wikipedia.org/wiki/Complex_number#Multiplication_and_division.

Parameters

mixed $c

Returns: Complex

Exceptions

Exception

◆ equals()

MathPHP\Number\Complex::equals ( Complex $c )

Test for equality Two complex numbers are equal if and only if both their real and imaginary parts are equal.

https://en.wikipedia.org/wiki/Complex_number#Equality

Parameters

Complex $c

Returns: bool

◆ inverse()

MathPHP\Number\Complex::inverse ( )

The inverse of a complex number (reciprocal)

https://en.wikipedia.org/wiki/Complex_number#Reciprocal

Returns: Complex

Exceptions

Exception

◆ multiply()

MathPHP\Number\Complex::multiply ( $c )

Complex multiplication https://en.wikipedia.org/wiki/Complex_number#Multiplication_and_division.

(a + bi)(c + di) = (ac - bd) + (bc + ad)i

Parameters

mixed $c

Returns: Complex

Exceptions

Exception

Implements MathPHP\Number\ObjectArithmetic.

◆ negate()

MathPHP\Number\Complex::negate ( )

Negate the complex number Switches the signs of both the real and imaginary parts.

Returns: Complex

◆ polarForm()

MathPHP\Number\Complex::polarForm ( )

Polar form https://en.wikipedia.org/wiki/Complex_number#Polar_form.

z = a + bi = r(cos(θ) + i sin(θ)) Where r = |z| θ = arg(z) (in radians)

Returns: Complex

◆ roots()

MathPHP\Number\Complex::roots ( )

The roots of a complex number https://en.wikipedia.org/wiki/Complex_number#Square_root.

The roots of a + bi (with b ≠ 0) are ±(γ + δi), where

    ____________
   /     _______
  / a + √a² + b²

γ = / ---------— √ 2

      ____________
     /      _______
    / -a + √a² + b²

δ = sgn(b) / ----------— √ 2

Returns: array Complex[] (two roots)

◆ sqrt()

MathPHP\Number\Complex::sqrt ( )

The square root of a complex number https://en.wikipedia.org/wiki/Complex_number#Square_root.

The roots of a + bi (with b ≠ 0) are ±(γ + δi), where

    ____________
   /     _______
  / a + √a² + b²

γ = / ---------— √ 2

      ____________
     /      _______
    / -a + √a² + b²

δ = sgn(b) / ----------— √ 2

The square root returns the positive root.

Returns: Complex (positive root)

◆ subtract()

MathPHP\Number\Complex::subtract ( $c )

Complex subtraction https://en.wikipedia.org/wiki/Complex_number#Addition_and_subtraction.

(a + bi) - (c + di) = (a - c) + (b - d)i

Parameters

mixed $c

Returns: Complex

Exceptions

Exception

Implements MathPHP\Number\ObjectArithmetic.

The documentation for this class was generated from the following file:

src/Number/Complex.php

Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ __construct()

Member Function Documentation

◆ __get()

◆ __toString()

◆ abs()

◆ add()

◆ arg()

◆ complexConjugate()

◆ divide()

◆ equals()

◆ inverse()

◆ multiply()

◆ negate()

◆ polarForm()

◆ roots()

◆ sqrt()

◆ subtract()