added complex number multiplication code in the string folder

Author: muskansngh07

src/main/java/com/thealgorithms/strings/ComplexNumberMultiplication.java

@@ -0,0 +1,65 @@
+package com.thealgorithms.strings;
+
+import java.util.Scanner;
+
+/**
+ * Implementation of complex number multiplication.
+ * 
+ * Given two strings representing complex numbers in the form "a+bi" and "c+di",
+ * this class provides a method to multiply them and return the result
+ * as a string in the same format.
+ *
+ * Example:
+ * Input: "1+1i", "1+1i"
+ * Output: "0+2i"
+ * 
+ *
+ * Formula used:
+ * (a + bi) × (c + di) = (ac - bd) + (ad + bc)i
+ **/
+
+public final class ComplexNumberMultiplication {
+
+    // Private constructor to prevent instantiation
+    private ComplexNumberMultiplication() {
+    }
+
+    /**
+     * Multiplies two complex numbers represented as strings.
+     *
+     * @param num1 The first complex number in the form "a+bi".
+     * @param num2 The second complex number in the form "c+di".
+     * @return The product of the two complex numbers as a string in the form "x+yi".
+     */
+    public static String complexNumberMultiply(String num1, String num2) {
+        // Split real and imaginary parts
+        String[] parts1 = num1.split("\\+");
+        String[] parts2 = num2.split("\\+");
+
+        int a = Integer.parseInt(parts1[0]);
+        int b = Integer.parseInt(parts1[1].replace("i", ""));
+        int c = Integer.parseInt(parts2[0]);
+        int d = Integer.parseInt(parts2[1].replace("i", ""));
+
+        // Apply the formula: (a+bi)*(c+di) = (ac - bd) + (ad + bc)i
+        int real = a * c - b * d;
+        int imag = a * d + b * c;
+
+        return real + "+" + imag + "i";
+    }
+
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+
+        System.out.print("Enter first complex number (a+bi): ");
+        String num1 = sc.nextLine();
+
+        System.out.print("Enter second complex number (c+di): ");
+        String num2 = sc.nextLine();
+
+        String result = complexNumberMultiply(num1, num2);
+        System.out.println("Result: " + result);
+
+        sc.close();
+    }
+}