Question

C++

PROBLEM STATEMENT: Devise an algorithm to perform the optimal multiplication of two complex numbers
SPECIFICATIONS: The multiplication of two complex numbers z1 = a+ bi and z2 = c+ di can be done in only three multiplications. Write an algorithm that uses only three multiplications (correct code, syntax)

Answer 1

// Code for Complex Multiplication in 3 steps
#include <iostream>
#include <string>
using namespace std;

void complex_multiplication(int a, int b, int c, int d, int ans[])
{
// (a + i * b) * (c + i * d) = (a * c - b * d) + i * (a * d + b * c)
// z1 = a + ib
// z2 = c + id
// Compute three real multiplications S1=ac, S2=bd, and S3=(a+b)(c+d)
// Compute the results as A=S1−S2 and B=S3−S1−S2

int s1, s2, s3;
s1 = a * c;
s2 = b * d;
s3 = (a+b)*(c+d);
ans[0] = s1 - s2;
ans[1] = s3-s1-s2;
}
  

int main()
{
int a,b,c,d;
a = 2;
b = 2;
c = 2;
d = 2;
// Driver Code for Complex Multiplication in 3 steps
int ans[2];
complex_multiplication(a, b, c, d, ans);
cout << "Real Part = " << ans[0] << " Imaginary Part = " << ans[1];
return 0;
}