A Complex Class

The following class encapsulates a complex number:


public class Complex
{
	private double re;  // real part
	private double im;  // imaginary part
	public Complex()  // default constructor 
	{
		re = im = 0;
	}
	public Complex(double a, double b)  // a + bi
	{

		re = a;
		im = b;
	}
	Complex add( Complex z)   
	{
//(a + bi)   + (c + di) = (a + b)  + (c + d)i.

		Complex sum = new Complex();
		sum.re = re + z.re;     
		sum.im = im + z.im;
		return sum;
	}

	Complex sub( Complex z)
	{
//(a + bi)   - (c + di) = (a - b)  + (c - d)i.

		Complex difference = new Complex();
		difference.re = re - z.re;
		difference.im = im - z.im;
		return difference;
	}

	Complex mul( Complex z)
	{
	               // (a + bi) *(c + di)  =  (ac – bd)  + (cb – ad)i
		Complex product = new Complex();
		product.re = re * z.re - im * z.im;   // (ac – bd)
		product.im = re * z.im + im * z.re;  // (cb – ad)
		return product;
	}

	double abs()
	{
		return Math.sqrt(re*re + im*im);
	}

	double real()
	{
		return re;
	}

	double imaginary()
	{
		return im;
	}
}


Complex Functions

Just as the function  h(x) = x2,, where x is a real number, pairs a real number, x, with its square, the complex valued function f(z) = z2 pairs a complex number z with its square.  For example,
	f(i) = i2 = -1
	f(2 + 3i) = (2+3i)*(2+3i) = (4 – 9) + (6 + 6) i = -5 + 12i
	f(3 + 7i) = (3 + 7i)(3 + 7i) = -40 + 42i

Similarly, if    f(z) = z2 + (3+ 2i) , then

		f(i) = i2 + (3 + 2i) = -1 + (3 + 2i) = 2 + 2i
		f(2+3i) = (2+3i)(2+3i)  + (3 + 2i) = (-5 + 12i) + (3 + 2i) = -2 + 14i

For example, a complex function such as f(z) = z2  and  f(z) = z2 + (3+ 2i)  can be implemented as:

public class ComplexFunctions
{
	public static Complex f(Complex z)
	{
		// f(z) = z* z
		return z.mul(z);
	}

	public static Complex g(Complex z)
	{
		// f(z) = z*z + (3 + 2i)
		Complex constant = new Complex(3,2); // 3 + 2i
		return   (z.mul(z)).add(constant);  // z*z + (3+2i)
 	}
}