Complex root function

[pjung-bosch]

Write a function in rust, that calculates all the n roots of a complex number

[github-actions[bot]]

🌟 Rust Function for Calculating N Roots of a Complex Number 🌟

Let's create a function in Rust to compute all the n roots of a given complex number. Here, we'll use Rust's num crate, which provides complex number support.

Step-by-Step Guide

1. Set up the environment 🛠️
2. Create the function 📐
3. Handle complex numbers and nth roots 🧮
4. Test the function 🔍

1. Set Up the Environment 🛠️

Start by adding the num crate to your Cargo.toml:

[dependencies]
num = "0.4"

2. Create the Function 📐

Below is the Rust code for calculating all n roots of a complex number:

extern crate num;
use num::complex::Complex;
use std::f64::consts::PI;

/// Calculate all n roots of a complex number
fn complex_n_roots(z: Complex<f64>, n: u32) -> Vec<Complex<f64>> {
    let mut roots = Vec::new();
    let r = z.norm().powf(1.0 / n as f64);
    let theta = z.arg();

    for k in 0..n {
        let angle = (theta + 2.0 * PI * k as f64) / n as f64;
        let root = Complex::from_polar(&r, &angle);
        roots.push(root);
    }
    roots
}

fn main() {
    let z = Complex::new(1.0, 1.0); // Example complex number
    let roots = complex_n_roots(z, 3); // Calculate cube roots

    for (i, root) in roots.iter().enumerate() {
        println!("Root {}: {}", i, root);
    }
}

3. Handle Complex Numbers and Nth Roots 🧮

When calculating nth roots of a complex number:

• r is the magnitude of the complex number z.
• θ (theta) is the argument (or angle) of the complex number z.
• The roots are calculated using the polar form of complex numbers, iterating for each of the n roots.

4. Test the Function 🔍

Here's how you can use and test the function with an example:

cargo run

You should see the roots of the complex number printed in the console.

🚀 Conclusion

And there you have it! A Rust function to calculate all n roots of a complex number. Feel free to experiment with different values of z and n. Happy coding! 👨‍💻👩‍💻