Complex Numbers & Functions

Supports Complex Numbers and Functions relating to Complex Numbers

Complex Numbers:

Complex Numbers are numbers that have both a real and imaginary part i. They are represented as a + bi where a is the real part and b is the imaginary part. i is the imaginary unit, where i^2 = -1.

Complex Numbers are supported by the struct Complex in the numerlib::Complex module. To create a new Complex Number, use the new() function.

Parameters:

real: The real part of the Complex Number, represented by a f64 value.
imag: The imaginary part of the Complex Number, represented by a f64 value.

Returns:

A new Complex Number, with the complex type.

Equation:

\[ a + bi \]

Example:

use numerilib::Complex;

fn main() {
    let z = Complex::new(1.0, 2.0);

    println!("Complex Number z: {}", z);
}

Executes as:

>>> Complex Number z: 1+2i

Returning Parts of a Complex Number:

Inorder to return the real or imaginary part of a Complex Number, use the .real_part() or imag_part() functions.

Parameters:

&self: The Complex Number to return the real or imaginary part of.

Returns:

The real or imaginary part of the Complex Number, represented by a f64 value.

Returning Real Value Example:

use numerilib::Complex;

fn main() {
    let z = Complex::new(1.0, 2.0);

    let real = z.real_part();
    
    println!("Real Part of z: {}", real);
}

Executes as:

>>> Real Part of z: 1

Returning Imaginary Value Example:

use numerilib::Complex;

fn main() {
    let z = Complex::new(1.0, 2.0);

    let imag = z.imag_part();
    
    println!("Imaginary Part of z: {}", imag);
}

Executes as:

>>> Imaginary Part of z: 2

The Magnitude of a Complex Number:

The Magnitude of a Complex Number is the distance from the origin to the Complex Number. It is represented by the absolute value of the Complex Number.

Parameters:

&self: The Complex Number to return the magnitude of.

use numerilib::Complex;

fn main() {
    let z = Complex::new(1.0, 2.0);

    let magnitude = z.magnitude();
    
    println!("Magnitude of z: {}", magnitude);
}

Executes as:

>>> Magnitude of z: 2.23606797749979 // √5

Complex Arithmetic:

Complex Arithmetic is supported by the Complex struct in the numerilib::Complex module. One Quick Notice: Complex Arithmetic can only be done by using operations in the Complex type.

Addition Example:

use numerilib::Complex;

fn main() {
    let a = Complex::new(3.0, 2.0);
    let b = Complex::new(1.0, 4.0);

    let sum = a + b;
    
    println!("Sum of 3+2i + 1+4i = {}", sum);
}

Executes as:

>>> Sum of 3+2i + 1+4i = 4+6i

Subtraction Example:

use numerilib::Complex;

fn main() {
    let a = Complex::new(3.0, 2.0);
    let b = Complex::new(1.0, 4.0);

    let difference = a - b;
    
    println!("Difference of 3+2i - 1+4i = {}", difference);
}

Executes as:

>>> Difference of 3+2i - 1+4i = 2-2i

Multiplication Example:

use numerilib::Complex;

fn main() {
    let a = Complex::new(3.0, 2.0);
    let b = Complex::new(1.0, 4.0);

    let product = a * b;
    
    println!("Product of 3+2i * 1+4i = {}", product);
}

Executes as:

>>> Product of 3+2i * 1+4i = -5+14i

Division Example:

use numerilib::Complex;

fn main() {
    let a = Complex::new(3.0, 2.0);
    let b = Complex::new(1.0, 4.0);

    let quotient = a / b;
    
    println!("Quotient of 3+2i / 1+4i = {}", quotient);
}

Executes as:

>>> Quotient of 3+2i / 1+4i = 0.5-0.5i

Power Raised to a `i32`:

use numerilib::Complex;

fn main() {
    let a = Complex::new(3.0, 2.0);

    let power = a.powi(2);
    
    println!("Power of 3+2i ^ 2 = {}", power);
}

Executes as:

>>> Power of 3+2i ^ 2 = 5+11.999999999999998i

Power Raised to a `f64`:

use numerilib::Complex;

fn main() {
    let a = Complex::new(3.0, 2.0);

    let power = a.powf(2_f64);
    
    println!("Power of 3+2i ^ 2 = {}", power);
}

Executes as:

>>> Power of 3+2i ^ 2 = 5+11.999999999999998i

NumeriLib Documentation