/* Imaginary Number class. */

#include <math.h>

class img {
public:

double r;
double i;
	img() {r=0.0; i=0.0;}
	img(double nr, double ni) {r=nr; i=ni;}	// constructor


inline img	operator * (img mul);
inline img	operator + (img mul);
inline img	operator - (img mul);
inline img	operator * (double mul);
inline img	operator + (double mul);
inline img	operator / (img div);
					// Now I know these are not correct functions (sin etc)
               // but who cares, they make wicked images

inline img 	sinimg() {img result(sin(r),sin(i));return result;}
inline img   cosimg() {img result(cos(r),cos(i));return result;}
inline img   cossinimg() {img result(cos(r),sin(i));return result;}
inline img   sincosimg() {img result(sin(r),cos(i));return result;}


inline img   tanimg() {img result(tan(r),tan(i));return result;}
inline img   atanimg() {img result(atan(r),atan(i));return result;}

};


inline img img::operator * (img mul) {                        // Multiplication
    img result(this->r * mul.r - (this->i*mul.i), this->r*mul.i + this->i*mul.r);
    return result;
}
inline img img::operator + (img mul) {								// Addition
    img result(this->r + mul.r, this->i + mul.i);
    return result;
}
inline img img::operator - (img mul) {								// Subtraction
    img result(this->r - mul.r, this->i - mul.i);
    return result;
}
inline img img::operator * (double mul) {                        // Multiplication  by a double (not correct)
    img result(this->r * mul, this->i * mul);
    return result;
}
inline img img::operator + (double mul) {                        // addition  by a double (not correct)
    img result(this->r + mul, this->i + mul);
    return result;
}
inline img img::operator / (img div) {                        // Dividing by another complex number
    img result(  (this->r*div.r + this->i*div.i)/(div.r*div.r + div.i*div.i),
    					(div.r*this->i - this->r*div.i)/(div.r*div.r + div.i*div.i)	);
    return result;
}