Step by Step solution about How to resolve the algorithm Roots of unity step by step in the Go programming language

This code in Go prints the roots of unity for the given value of n which corresponds to the number of roots. The roots of unity are complex numbers that satisfy the equation z^n = 1 for some integer n. They are evenly distributed on the unit circle in the complex plane.

The main function calls the roots function for n values ranging from 2 to 5, inclusive. The roots function creates a slice of complex numbers and then loops over the range of n values, calculating the roots of unity for each value and storing them in the slice. The roots function uses the cmplx.Rect function to create a complex number with a given magnitude and phase angle. The magnitude is set to 1, and the phase angle is set to 2*math.Pi*float64(i)/float64(n) where i is the loop index and n is the number of roots. The main function then prints the roots of unity for each value of n using the fmt.Printf function. The format string " %18.15f\n" specifies that the complex numbers should be printed with 18 characters of width, 15 of which are after the decimal point.

Here is an example of the output of the program:

2 roots of 1:
  -1.000000000000000 +0.000000000000000i
   1.000000000000000 +0.000000000000000i
3 roots of 1:
  -0.500000000000000 -0.866025403784438i
   1.000000000000000 +0.000000000000000i
  -0.500000000000000 +0.866025403784438i
4 roots of 1:
   0.000000000000000 -1.000000000000000i
   1.000000000000000 +0.000000000000000i
  -0.000000000000000 -1.000000000000000i
   1.000000000000000 +0.000000000000000i
5 roots of 1:
  -0.309016994374947 -0.951056516295154i
   0.809016994374947 -0.587785252292473i
   1.000000000000000 +0.000000000000000i
   0.809016994374947 +0.587785252292473i
  -0.309016994374947 +0.951056516295154i

package main

import (
    "fmt"
    "math"
    "math/cmplx"
)

func main() {
    for n := 2; n <= 5; n++ {
        fmt.Printf("%d roots of 1:\n", n)
        for _, r := range roots(n) {
            fmt.Printf("  %18.15f\n", r)
        }
    }
}

func roots(n int) []complex128 {
    r := make([]complex128, n)
    for i := 0; i < n; i++ {
        r[i] = cmplx.Rect(1, 2*math.Pi*float64(i)/float64(n))
    }
    return r
}