void setup() {
   Complex c1 = new Complex(1,2);
   Complex c2 = new Complex(3,4);
   Complex m = Complex.cMult(c1,c2);
   println("c1 = " + c1 + "  c2 = " + c2 + "  c1*c2 = " + m);
}

//**********************************************************
static class Complex {
  float real = 0;
  float imag= 0;

  Complex() {
  }

  Complex(Complex c) {
    real = c.real;
    imag = c.imag;
  }

  Complex (float r, float i) {
    real = r;
    imag = i;
  }

  static Complex conjugate(Complex c) {
    return new Complex(c.real, - c.imag);
  }

  static Complex cMult(Complex c1, Complex c2) {
    float realPart = c1.real*c2.real-c1.imag*c2.imag;
    float imagPart = c1.real*c2.imag + c2.real*c1.imag;
    return new Complex(realPart,imagPart);
  }

/*
  // Adds two complex numbers, c1 + c2
  static Complex cAdd(Complex c1, Complex c2) {
    // Add your code here
  }
  
  // Subtracts two complex numbers, c1 - c2
  static Complex cSub(Complex c1, Complex c2) {
    // Add your code here
  }
  
  
  // Divides two complex numbers, c1 / c2
  static Complex cDiv(Complex c1, Complex c2) {
    // Add your code here
  }
*/


  // convert polar coordinates to Cartesian coordinates.
  static Complex polar2Cart(float r, float degrees) {
    float realPart = r*cos(radians(degrees));
    float imagPart = r*sin(radians(degrees));
    return new Complex(realPart,imagPart); 
  }

  static float len(Complex c) {
    return sqrt(c.real*c.real+ c.imag*c.imag);
  }

  static float angle(Complex c) {
    if (c.real==0 && c.imag == 0) return 0;
    else if (c.real >= 0) return asin( c.imag/len(c));
    else return PI-asin(c.imag/len(c));
  }

  float  zAbs() {
    return real*real + imag*imag;
  }

  String toString() {
    return real + " + " + imag + "i"; 
  }
}