original ) (raw )Last Updated : 13 Jul, 2022
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.
class ComplexNumber {
`` int real, image;
`` public ComplexNumber( int r, int i)
`` {
`` this .real = r;
`` this .image = i;
`` }
`` public void showC()
`` {
`` System.out.println( this .real + " +i " + this .image);
`` }
`` 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:
class ComplexNumber {
`` int real, image;
`` public ComplexNumber( int r, int i)
`` {
`` this .real = r;
`` this .image = i;
`` }
`` public void showC()
`` {
`` System.out.print( this .real + " +i" + this .image);
`` }
`` public static ComplexNumber add(ComplexNumber n1,
`` ComplexNumber n2)
`` {
`` ComplexNumber res = new ComplexNumber( 0 , 0 );
`` res.real = n1.real + n2.real;
`` res.image = n1.image + n2.image;
`` return res;
`` }
`` public static void main(String arg[])
`` {
`` ComplexNumber c1 = new ComplexNumber( 4 , 5 );
`` ComplexNumber c2 = new ComplexNumber( 10 , 5 );
`` System.out.print( "first Complex number: " );
`` c1.showC();
`` System.out.print( "\nSecond Complex number: " );
`` c2.showC();
`` ComplexNumber res = add(c1, c2);
`` 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)
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