package class7_3_Complex;

/**
 * A complex number.
 *
 * This number consists of two parts, the real part
 * (an ordinary number with a decimal part)
 * and the imaginary part (an ordinary number
 * multiplied by sqrt(-1).
 *
 * The full number is
 *   real + imag * i
 *
 * where i = sqrt(-1)
 */
public class Complex {
    private double real;
    private double imag;
    /**
     * Create a complex zero.
     * Both real and imaginary parts are zero
     */
    public Complex() {
        this(0,0); // DIFFERENT FROM: new Complex(0,0) <- DOESN'T WORK
    }

    /**
     * Create a real number. The imaginary part is zero.
     * @param real The value of the real number
     */
    public Complex(double real) {
        // Exercise: ??? What goes here ???
    }

    /**
     * Create a complex number
     * @param real The real part of the number
     * @param imag The imaginary part of the number
     */
     public Complex(double real, double imag) {
         this.real = real;
         this.imag = imag;
     }

    /**
     * Multiply this complex number by the other one.
     * @param other The other complex number to multiply by. Must not be null.
     * @return a new complex object holding the result
     */
    public Complex multBy(Complex other) {
        Complex result = new Complex();
        result.real = this.real * other.real - this.imag * other.imag;
        result.imag = this.real * other.imag + this.imag * other.real;
        return result;
    }

    /**
     * @return This number, formatted similar to "4.5 + 3.4 i"
     */
    public String toString() {
        // Exercise: Print 4.0 i as 4 i instead of 0.0 + 4.0i
        return real + " + " + imag + "i";
    }
}