Step by Step solution about How to resolve the algorithm Euler's identity step by step in the C# programming language

This code demonstrates the uses of System.Numerics library for working with complex numbers. Specifically, it evaluates the famous mathematical expression e^(iπ) + 1

• Complex e = Math.E creates a Complex object representing the mathematical constant e(Euler's number)

• Complex i = Complex.ImaginaryOne; creates a Complex object representing the imaginary unit i(where i^2 = -1).

• Complex π = Math.PI: creates a Complex representing the mathematical constant pi(the ratio of a circle's circumference to its diameter)

• Console.WriteLine(Complex.Pow(e, i * π) + 1);

• Complex.Pow(e, i * π) calculates e to the power of iπ using the built-in Pow method.

• + 1: adds 1 to the result of the exponentiation.

• This line evaluates the expression e^(iπ) + 1 and prints the result to the console.

The expected output of this code is 1+0E-20i which represents the complex number 1 with a very small imaginary component close to zero. This result confirms Euler's identity, which states that e^(iπ) + 1 = 0.

using System;
using System.Numerics;

public class Program
{
    static void Main() {
        Complex e = Math.E;
        Complex i = Complex.ImaginaryOne;
        Complex π = Math.PI;
        Console.WriteLine(Complex.Pow(e, i * π) + 1);
    }
}