Problem Statement

In mathematics, Euler's identity is the equality: where Euler's identity is often cited as an example of deep mathematical beauty. Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants: Show in your language that Euler's identity is true. As much as possible and practical, mimic the Euler's identity equation. Most languages are limited to IEEE 754 floating point calculations so will have some error in the calculation. If that is the case, or there is some other limitation, show that ei

π

{\displaystyle \pi }

• 1 is approximately equal to zero and show the amount of error in the calculation. If your language is capable of symbolic calculations, show that ei

π

{\displaystyle \pi }

• 1 is exactly equal to zero for bonus kudos points.

Let's start with the solution:

import spire.math.{Complex, Real}

object Scratch extends App{
  //Declare values with friendly names to clean up the final expression
  val e = Complex[Real](Real.e, 0)
  val pi = Complex[Real](Real.pi, 0)
  val i = Complex[Real](0, 1)
  val one = Complex.one[Real]
  
  println(e.pow(pi*i) + one)
}