Java Program to Add two Complex Numbers
Last Updated :
13 Jul, 2022
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Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra. The standard format for complex numbers is a + bi, with the real number first and the imaginary number last.
General form for any complex number is:
a+ib Where "a" is real number and "b" is Imaginary number.
Construction of Complex number
For creating a complex numbers, we will pass imaginary numbers and real numbers as parameters for constructors.
// Java program to construct the complex number
class ComplexNumber {
// variables to hold real and imaginary part of complex
// number
int real, image;
// Constructor which will be used while creating complex
// number
public ComplexNumber(int r, int i)
{
this.real = r;
this.image = i;
}
// function to print real number
public void showC()
{
System.out.println(this.real + " +i " + this.image);
}
// we will implement this function for addition
public complex add(ComplexNumber, ComplexNumber);
}
Time Complexity: O(1)
Auxiliary Space: O(1)
Add function
- Basically, addition of two complex numbers is done by adding real part of the first complex number with real part of the second complex number.
- And adding imaginary part of the first complex number with the second which results into the third complex number.
- So that means our add() will return another complex number.
Ex. addition of two complex numbers
(a1) + (b1)i -----(1)
(a2)+ (b2)i -----(2)
adding (1) and (2) will look like
(a1+a2) + (b1+b2)i
Function Definition:
ComplexNumber add(ComplexNumber n1, ComplexNumber n2){
ComplexNumber res = new ComplexNumber(0,0); //creating blank complex number
// adding real parts of both complex numbers
res.real = n1.real + n2.real;
// adding imaginary parts
res.image = n1.image + n2.image;
// returning result
return res;
}
Code:
// Java program to add two complex numbers
class ComplexNumber {
// variables to hold real and imaginary part of complex
// number
int real, image;
// Constructor which will be used while creating complex
// number
public ComplexNumber(int r, int i)
{
this.real = r;
this.image = i;
}
// function to print real number
public void showC()
{
System.out.print(this.real + " +i" + this.image);
}
// function for addition
public static ComplexNumber add(ComplexNumber n1,
ComplexNumber n2)
{
// creating blank complex number
// to store result
ComplexNumber res = new ComplexNumber(0, 0);
// adding real parts of both complex numbers
res.real = n1.real + n2.real;
// adding imaginary parts
res.image = n1.image + n2.image;
// returning result
return res;
}
public static void main(String arg[])
{
// creating two complex numbers
ComplexNumber c1 = new ComplexNumber(4, 5);
ComplexNumber c2 = new ComplexNumber(10, 5);
// printing complex numbers
System.out.print("first Complex number: ");
c1.showC();
System.out.print("\nSecond Complex number: ");
c2.showC();
// calling add() to perform addition
ComplexNumber res = add(c1, c2);
// displaying addition
System.out.println("\nAddition is :");
res.showC();
}
}
Output
first Complex number: 4 +i5 Second Complex number: 10 +i5 Addition is : 14 +i10
Time Complexity: O(1)
Auxiliary Space: O(1)
