Step by Step solution about How to resolve the algorithm Roots of unity step by step in the Mathematica/Wolfram Language programming language

The provided Wolfram language code defines a function called RootsUnity that generates the nth roots of unity, which are complex numbers that are equally spaced around the unit circle.

Here is the breakdown of the code:

1. Function Signature:

   RootsUnity[nthroot_Integer?Positive] :=
   

   • This line defines the function RootsUnity, which takes one argument, nthroot.
   • nthroot must be a positive integer and specifies the number of roots to generate.

2. Function Body:

   Table[Exp[2 Pi I i/nthroot], {i, 0, nthroot - 1}]
   

   • This line is the main part of the function and generates the nth roots of unity.
   • Table creates a list of values generated by the expression inside the curly braces.
   • Exp[2 Pi I i/nthroot] calculates the nth root of unity for integer values of i ranging from 0 to nthroot - 1.
   • 2 Pi I is the complex number representing a full circle on the unit circle.
   • Dividing 2 Pi I by nthroot and multiplying it by i gives the angle for each root of unity, ensuring equal spacing around the unit circle.

Example:

To generate the 5th roots of unity, you can use the following code:

RootsUnity[5]

Output:

{1., -0.809017 + 0.587785 I, -0.587785 - 0.809017 I, 0.587785 + 0.809017 I, 0.809017 - 0.587785 I}

This list of complex numbers represents the 5th roots of unity, which are equally spaced around the unit circle.

RootsUnity[nthroot_Integer?Positive] := Table[Exp[2 Pi I i/nthroot], {i, 0, nthroot - 1}]