// Represents a complex number of the form
//
//    a + i * b
//
// Where i is the imaginary unit.
class Complex {
  // real part
  private double a;
  // imaginary part
  private double b;
  
  // Construct a new complex number with real part a and
  // imginary part b.
  public Complex(double a, double b) {
    this.a = a;
    this.b = b;
  }
  
  // Returns a new complex number which is the sum of this
  // number and the passed number.
  public Complex add(Complex other) {
    return new Complex(this.a + other.a, this.b + other.b);
  }
  
  // Returns a squared version of this number.
  public Complex square() {
    return new Complex(
        this.a * this.a - this.b * this.b,
        this.a * this.b + this.a * this.b);
  }
  
  // Returns the magnitude of this number, defined as the
  // square root of a^2 + b^2.
  public double magnitude() {
    return Math.sqrt(a * a + b * b);
  }
  
  // Returns a String representation of the complex number.
  public String toString() {
    return this.a + " + i * " + this.b;
  }
}