Complex Numbers

Complex numbers are quite essential mathematical abstraction: whether one beleives it or not. They are extensively used in applied mathematics and play an important role in many branches of science. These models typically require extensive computations involving manipulating complex numbers according to well-defined arithmetic operations, so we want to write a program to do the computations. In short we need a new datatype 'Complex'.

 The basic operations on complex nubers are: additon, substraction, multiplication, division, finding reciprocal, absolute value, square root, conjugate, and converting to polar form.

 Let us write a program which will create a new datatype complex that will do the above operations and another program to test our new datatype.

class Complex

{

    double r,i;

    Complex()

    {

        r=0;

        i=0;

    }

    Complex(double real, double imag)

    {

        r = real;

        i = imag;

    }

    Complex plus(Complex b)

    {

        Complex c=new Complex();

        c.r=r+b.r;

        c.i=i+b.i;

        return c;

    }

    Complex minus(Complex b)

    {

        Complex c=new Complex();

        c.r=r-b.r;

        c.i=i-b.i;

        return c;

    }

    Complex times(Complex b)

    {

        Complex c=new Complex();

        c.r=r*b.r-i*b.i;

        c.i=r*b.i+i*b.r;

        return c;

    }

    double abs()

    {

        double a=Math.sqrt(r*r+i*i);

        return a;

    }

    double Re()

    {

        return r;

    }

    double Im()

    {

        return i;

    }

    public String toString()

    {

        if(i>=0)

        return Re()+"+"+Im()+"i";

        else

        return Re()+"-"+(-Im())+"i";

    }

    String polar()

    {

        double amp,arg;

        amp=abs();

        arg=Math.atan(i/r);

        double x=Math.PI/arg;

        return(amp+"*cis("+x+")");

    }

    Complex sqrt()

    {

        Complex c=new Complex();

        c.r=Math.sqrt((abs()+r)/2);

        c.i=Math.sqrt((abs()-r)/2);

        return c;

    }

    Complex conjg()

    {

        Complex c=new Complex();

        c.r=r;

        c.i=-i;

        return c;

    }

    Complex divideBy(Complex b)

    {

        Complex cb=new Complex(0,0),c=new Complex(0,0);

        double d;

        cb=b.conjg();

        c.r=r*cb.r-i*cb.i;

        c.i=i*cb.r+r*cb.i;

        d=cb.r*cb.r+cb.i*cb.i;

        c.r /= d;

        c.i /= d;

        return c;

    }

    Complex inv()

    {

        Complex c=new Complex();

        double d=r*r+i*i;

        c=conjg();

        c.r=c.r/d;

        c.i=c.i/d;

        return c;

    }

    Complex pow(int a)

    {

        Complex c=new Complex(r,i);

        int b=(a>0)?a:-a;

        if(a==0)

        {

            c.r=1;

            c.i=0;

        }

        else

        {

            for(int i=1;i<b;i++)

            {

                c=times(c);

            }

        }

        if(a<0)

        c=c.inv();

        return c;

    }

}

import java.io.*;

class TestComplexNumber

{

    public static void main(String arg[])throws IOException

    {

        BufferedReader x=new BufferedReader(new InputStreamReader(System.in));

        Complex A=new Complex(),B=new Complex(),C=new Complex();

        System.out.println("Enter real part and imaginary part of A");

        A.r=Double.parseDouble(x.readLine());

        A.i=Double.parseDouble(x.readLine());

        System.out.println("Enter real part and imaginary part of B");

        B.r=Double.parseDouble(x.readLine());

        B.i=Double.parseDouble(x.readLine());

        System.out.println("Enter a number");

        int n=Integer.parseInt(x.readLine());

        System.out.println("\f");

        System.out.println("A="+A.toString());

        System.out.println("B="+B.toString());

        C=A.plus(B);

        System.out.print("A+B="+C.toString()+"\n");

        C=A.minus(B);

        System.out.print("A-B="+C.toString()+"\n");

        C=A.times(B);

        System.out.print("A*B="+C.toString()+"\n");

        C=A.divideBy(B);

        System.out.print("A/B="+C.toString()+"\n");

        C=A.conjg();

        System.out.print("Conjugate of A="+C.toString()+"\n");

        C=B.conjg();

        System.out.print("Conjugate of B="+C.toString()+"\n");

        double a=A.abs();

        System.out.print("Absolute value of A="+a+"\n");

        double b=B.abs();

        System.out.print("Absolute value of B="+b+"\n");

        C=A.inv();

        System.out.print("Reciprocal value of A="+C.toString()+"\n");

        C=B.inv();

        System.out.print("Reciprocal value of B="+C.toString()+"\n");

        C=A.sqrt();

        System.out.print("Square root of A="+C.toString()+"\n");

        C=B.sqrt();

        System.out.print("Square root of B="+C.toString()+"\n");

        C=A.pow(n);

        System.out.print("A^"+n+"="+C.toString()+"\n");

        C=B.pow(n);

        System.out.print("B^"+n+"="+C.toString()+"\n");

        String a1=A.polar();

        System.out.print("Polar form of A="+a1+"\n");

        String b1=B.polar();

        System.out.print("Polar form of B="+b1+"\n");

    }

}