/****************************************
* Section : 15
* Machine No. : N
* Roll No. : 19CS100XY
* Name : Aritra Hazra
* Assignment No : 1
* Description : Complex Number Operations
*****************************************/

#include <stdio.h>
#include <math.h>

int main ()
{
    double r1, r2, i1, i2, r, i;

    /* taking real and imaginary parts of a complex number from user as inputs */
    printf("++ Enter Complex Number-1 ++\n");
    printf("\t-- Real Part: ");
    scanf("%lf", &r1);
    printf("\t-- Imaginary Part: ");
    scanf("%lf", &i1);
    printf("++ Enter Complex Number-2 ++\n");
    printf("\t-- Real Part: ");
    scanf("%lf", &r2);
    printf("\t-- Imaginary Part: ");
    scanf("%lf", &i2);
    
    /* printing the two complex numbers in (a+bi) format */
    printf("\n** Complex Number-1: C1 = (%lf) + (%lf)i", r1, i1);
    printf("\n** Complex Number-2: C2 = (%lf) + (%lf)i\n", r2, i2);
    
    /* computing the modulus of two complex numbers */
    printf("\n** Modulus of Complex Number-1: |C1| = %lf", sqrt(r1*r1+i1*i1));
    printf("\n** Modulus of Complex Number-2: |C2| = %lf", sqrt(r2*r2+i2*i2));
    
    /* computing the conjugate of two complex numbers */
    printf("\n** Conjugate of Complex Number-1: ~C1 = (%lf) + (%lf)i", r1, -i1);
    printf("\n** Conjugate of Complex Number-2: ~C2 = (%lf) + (%lf)i", r2, -i2);
    
    /* computing the arguement of two complex numbers */
    printf("\n** Argument of Complex Number-1: arg(C1) = %lf", atan(i1/r1));
    printf("\n** Argument of Complex Number-2: arg(C2) = %lf", atan(i2/r2));
    
    /* adding two complex numbers */
    r = (r1+r2); i = (i1+i2);
    printf("\n** Complex Number after ADDITION: (C1 + C2) = (%lf) + (%lf)i", r, i);
    
    /* subtracting two complex numbers */
    r = (r1-r2); i = (i1-i2);
    printf("\n** Complex Number after SUBTRACTION: (C1 - C2) = (%lf) + (%lf)i", r, i);
    
    /* multiplying two complex numbers */
    r = (r1*r2-i1*i2); i = (r1*i2+r2*i1);
    printf("\n** Complex Number after MULTIPLICATION: (C1 x C2) = (%lf) + (%lf)i", r, i);
    
    /* dividing two complex numbers */
    r = (r1*r2+i1*i2)/(r2*r2+i2*i2); i = (r2*i1-r1*i2)/(r2*r2+i2*i2);
    printf("\n** Complex Number after DIVISION: (C1 / C2) = (%lf) + (%lf)i", r, i);
    
    /* computing the squares of two complex numbers */
    r = (r1*r1-i1*i1); i = 2*r1*i1;
    printf("\n** SQUARE of Complex Number-1: C1^2 = (%lf) + (%lf)i", r, i);
    r = (r2*r2-i2*i2); i = 2*r2*i2;
    printf("\n** SQUARE of Complex Number-2: C2^2 = (%lf) + (%lf)i", r, i);
    
    /* computing the cubes of two complex numbers */
    r = (r1*r1*r1-3*r1*i1*i1); i = (3*r1*r1*i1-i1*i1*i1);
    printf("\n** CUBE of Complex Number-1: C1^3 = (%lf) + (%lf)i", r, i);
    r = (r2*r2*r2-3*r2*i2*i2); i = (3*r2*r2*i2-i2*i2*i2);
    printf("\n** CUBE of Complex Number-2: C2^3 = (%lf) + (%lf)i", r, i);
    
    /* computing the square-roots of two complex numbers */
    r = sqrt((r1+sqrt(r1*r1+i1*i1))/2); i = ((i1>=0)-(i1<0))*sqrt((-r1+sqrt(r1*r1+i1*i1))/2);
    printf("\n** SQUARE ROOT of Complex Number-1: SQRT(C1) = (+/-) [(%lf) + (%lf)i]", r, i);
    r = sqrt((r2+sqrt(r2*r2+i2*i2))/2); i = ((i2>=0)-(i2<0))*sqrt((-r2+sqrt(r2*r2+i2*i2))/2);
    printf("\n** SQUARE ROOT of Complex Number-2: SQRT(C2) = (+/-) [(%lf) + (%lf)i]", r, i);
    
    /* computing the reciprocals of two complex numbers */
    r = r1/(r1*r1+i1*i1); i = -i1/(r1*r1+i1*i1);
    printf("\n** RECIPROCAL of Complex Number-1: 1/C1 = (%lf) + (%lf)i", r, i);
    r = r2/(r2*r2+i2*i2); i = -i2/(r2*r2+i2*i2);
    printf("\n** RECIPROCAL of Complex Number-2: 1/C2 = (%lf) + (%lf)i", r, i);
    
    /* computing the exponentiation of two complex numbers (with respect to 'e') */
    r = exp(r1)*cos(i1); i = exp(r1)*sin(i1);
    printf("\n** EXPONENTIATION of Complex Number-1: e^C1 = (%lf) + (%lf)i", r, i);
    r = exp(r2)*cos(i2); i = exp(r2)*sin(i2);
    printf("\n** EXPONENTIATION of Complex Number-2: e^C2 = (%lf) + (%lf)i\n", r, i);
    
    return (0);
}