Complex.md

Complex

This is the Complex class version 1.0.

Represents a complex number.

Ferret has native support for complex numbers, including syntax for the normal mathematic notation in rectangular form a + bi, where a and b are real numbers and i is the imaginary unit. a and b are commonly called the "real part" and "imaginary part" respectively, despite both being real numbers.

Complex numbers can also be constructed from polar representations r(cosθ + isinθ) or re^(iθ) with Complex.polar().

Initializer

$z = Complex($a: Num, $b: Num)

Creates a complex number with the given real and imaginary parts. This is only useful to create a complex number from variable parts, since Ferret has native support for inline a + bi notation.

If the given imaginary part is zero, the constructor returns the real part as a real number.

• a: Num - Real part.

• b: Num - Imaginary part (a real number, though).

Initializer

$z = Complex($r: Num, $θ: Num)

Create a complex number in polar form given radius r and angle θ.

z = r(cosθ + isinθ).

• r: Num - Distance from the origin in the complex plane.

• θ: Num - Angle between the positive real axis and the.

Methods

abs

$z.abs

Computed property. Absolute value (or modulus) of the complex number. This is distance from the origin on the complex plane.

In polar form, this is r.

arg

$z.arg

Computed property. Argument of the complex number. On the complex plane, this is the angle θ between the positive real axis and the position vector.

In polar form, this is θ.

conj

$z.conj

Computed property. Conjugate of the complex number.

sqrt

$z.sqrt

Computed property. Square root of the complex number.

root

$z.root($n: Num)

Nth root of the complex number.

• n: Num

Addition operator (+)

$z + ($rhs: Complex)

Addition of complex numbers.

Addition operator (+)

$z + ($ehs: Num)

Addition of complex and real numbers.

Subtraction operator (-)

$z - ($rhs: Complex)

Subtraction of complex numbers.

Subtraction operator (-)

$z - ($rhs: Num)

Subtraction of real number from complex number.

Subtraction operator (-)

$z - ($lhs: Num)

Subtraction of complex number from real number.

Multiplication operator (*)

$z * ($rhs: Complex)

Multiplication of complex numbers.

Multiplication operator (*)

$z * ($ehs: Num)

Multiplication of real and complex numbers.

Division operator (/)

$z / ($rhs: Complex)

Division of complex numbers.

Division operator (/)

$z / ($rhs: Num)

Division of complex number by real number.

Exponent operator (^)

$z ^ ($rhs: Num)

Complex number to real power.

This can get expensive for large powers. For a quicker but less precise alternative, use .pow().

Exponent operator (^)

$z ^ ($lhs: Num)

Real number to a complex power.

Equality operator (==)

$z == ($ehs: Complex)

Equality of complex numbers.

Equality operator (==)

$z == ($ehs: Num)

Equality of complex number and real number.

pow

$z.pow($rhs: Num)

Complex number to real power. This is an alternative implementation to the power operator which is faster but less precise.

• rhs: Num

Class functions

polar

Complex.polar($r: Num, $θ: Num)

Create a complex number in polar form given radius r and angle θ.

z = r(cosθ + isinθ).

• r: Num - Distance from the origin in the complex plane.

• θ: Num - Angle between the positive real axis and the.

End of the Complex class.

This file was generated automatically by the Ferret compiler from Complex.frt.