#include <math.h>


typedef struct _mycomplex {
    float re;
    float im;
} Complex;


inline Complex complex_new(float re, float im) __attribute__ ((always_inline));
inline Complex complex_add(Complex c1, Complex c2)  __attribute__ ((always_inline));
inline Complex complex_mult(Complex c1, Complex c2)  __attribute__ ((always_inline));
inline double complex_abs(Complex c) __attribute__ ((always_inline));

inline Complex complex_new(float re, float im)
{
    Complex c;
    c.re = re;
    c.im = im;
    return c;
}

inline Complex complex_mult(Complex c1, Complex c2)
{
    Complex ret;
    ret.re = c1.re * c2.re - c1.im * c2.im;
    ret.im = c1.re * c2.im + c1.im * c2.re;
    return ret;
}

inline Complex complex_add(Complex c1, Complex c2)
{
    c1.re += c2.re;
    c1.im += c2.im;
    return c1;
}

inline Complex complex_conj(Complex c) {
    c.im = -c.im;
    return c;
}

inline double complex_abs(Complex c)
{
    double re, im;
    re = c.re;
    im = c.im;
    return sqrt(re * re + im * im);
}

inline void complex_print(Complex c) {
    printf("%.3f + i%.3f", c.re, c.im);
}