Multiplication of two complex numbers given as strings

Difficulty Level : Easy
Last Updated : 08 Feb, 2021

Given two complex numbers in the form of string. Our task is to print the multiplication of these two complex numbers.

Examples:

Input : str1 = "1+1i"
        str2 = "1+1i" 
Output : "0+2i"
Here, (1 + i) * (1 + i) = 
1 + i2 + 2 * i = 2i or "0+2i"

Input : str1 = "1+-1i"
        str2 = "1+-1i"
Output : "0+-2i"
Here, (1 - i) * (1 - i) = 
1 + i2 - 2 * i = -2i or "0+-2i"

Multiplication of two complex numbers can be done as:
$(a+ib) \times (x+iy)=ax+i^2by+i(bx+ay)=ax-by+i(bx+ay)$

We simply split up the real and the imaginary parts of the given complex strings based on the ‘+’ and the ‘i’ symbols. We store the real parts of the two strings a and b as x[0] and y[0] respectively and the imaginary parts as x[1] and y[1] respectively. Then, we multiply the real and the imaginary parts as required after converting the extracted parts into integers. Then, we again form the return string in the required format and return the result.

Java

// Java program to multiply two complex numbers
// given as strings.
import java.util.*;
import java.lang.*;
 
public class GfG{
    public static String complexNumberMultiply(String a, String b) {
 
        // Spiting the real and imaginary parts
        // of the given complex strings based on '+'
        // and 'i' symbols.
        String x[] = a.split("\\+|i");
        String y[] = b.split("\\+|i");
         
        // Storing the real part of complex string a
        int a_real = Integer.parseInt(x[0]);
         
        // Storing the imaginary part of complex string a
        int a_img = Integer.parseInt(x[1]);
         
        // Storing the real part of complex string b
        int b_real = Integer.parseInt(y[0]);
         
        // Storing the imaginary part of complex string b
        int b_img = Integer.parseInt(y[1]);
         
        // Returns the product.
        return (a_real * b_real - a_img * b_img) + "+" +
              (a_real * b_img + a_img * b_real) + "i";
    }
     
    // Driver function 
    public static void main(String argc[]){
        String str1 = "1+1i";
        String str2 = "1+1i";
        System.out.println(complexNumberMultiply(str1, str2));
    }
}

C++

// C++ Implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
string complexNumberMultiply(string a, string b)
{
    int i;
    string x1;
    int temp = 1;
 
    // Traverse both strings, and 
    // check for negative numbers
    for (i = 0; i < a.length(); i++) 
    {
        if (a[i] == '+')
            break;
        if (a[i] == '-')
        {
            temp = -1;
            continue;
        }
        x1.push_back(a[i]);
    }
     
    // String to int
    int t1 = stoi(x1) * temp;
    x1.clear();
    temp = 1;
    for (; i < a.length() - 1; i++) 
    {
        if (a[i] == '-')
        {
            temp = -1;
            continue;
        }
        x1.push_back(a[i]);
    }
    int t2 = stoi(x1) * temp;
    x1.clear();
    temp = 1;
    for (i = 0; i < b.length(); i++)
    {
        if (b[i] == '+')
            break;
        if (b[i] == '-')
        {
            temp = -1;
            continue;
        }
        x1.push_back(b[i]);
    }
    int t3 = stoi(x1) * temp;
    x1.clear();
    temp = 1;
    for (; i < b.length() - 1; i++) 
    {
        if (b[i] == '-') 
        {
            temp = -1;
            continue;
        }
        x1.push_back(b[i]);
    }
    int t4 = stoi(x1) * temp;
    
    // Real Part
    int ans = t1 * t3 - t2 * t4;
    string s;
    s += to_string(ans);
    s += '+';
     
    // Imaginary part
    ans = t1 * t4 + t2 * t3;
    s += to_string(ans);
    s += 'i';
 
    // Return the result
    return s;
}
 
  
// Driver Code
int main()
{
 
    string str1 = "1+1i";
    string str2 = "1+1i";
    cout << complexNumberMultiply(str1, str2);
 
    return 0;
 
    // Contributed By Bhavneet Singh
}

Python 3

# Python 3 program to multiply two complex numbers
# given as strings.
def complexNumberMultiply(a, b):
     
    # Spiting the real and imaginary parts
    # of the given complex strings based on '+'
    # and 'i' symbols.
    x = a.split('+')
    x[1] = x[1][:-1] # for removing 'i'
     
    y = b.split("+")
    y[1] = y[1][:-1] # for removing 'i'
     
    # Storing the real part of complex string a
    a_real = int(x[0])
         
    # Storing the imaginary part of complex string a
    a_img = int(x[1])
     
         
    # Storing the real part of complex string b
    b_real = int(y[0])
     
         
    # Storing the imaginary part of complex string b
    b_img = int(y[1])
    return str(a_real * b_real - a_img * b_img) \
        + "+" + str(a_real * b_img + a_img * b_real) + "i";
 
     
# Driver function 
 
str1 = "1 + 1i"
str2 = "1 + 1i"
print(complexNumberMultiply(str1, str2))
 
# This code is contributed by ANKITKUMAR34

PHP

<?php
// PHP program to multiply 
// two complex numbers
// given as strings.
 
function complexNumberMultiply($a, $b) 
{
 
// Spiting the real and 
// imaginary parts of the
// given complex strings 
// based on '+' and 'i' symbols.
$x = preg_split("/[\s+]+|i/" , $a);
$y = preg_split("/[\s+]+|i/" , $b);
     
// Storing the real part
// of complex string a
$a_real = intval($x[0]);
     
// Storing the imaginary 
// part of complex string a
$a_img = intval($x[1]);
     
// Storing the real part 
// of complex string b
$b_real = intval($y[0]);
     
// Storing the imaginary 
// part of complex string b
$b_img = intval($y[1]);
     
// Returns the product.
return ($a_real * $b_real - 
        $a_img * $b_img) . "+" . 
       ($a_real * $b_img + 
        $a_img * $b_real) . "i";
}
 
// Driver Code
$str1 = "1+1i";
$str2 = "1+1i";
echo complexNumberMultiply($str1, $str2);
 
// This code is contributed by mits
?>

Output:

0+2i

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