C Complex Numbers (<complex.h>)

Key Complex Number Concepts

float complex fc;
double complex dc;
long double complex ldc;

double r = creal(z);
double i = cimag(z);

double mag = cabs(z);
double phase = carg(z);

complex double result = csqrt(z);
complex double exp_z = cexp(z);

🔹 Basic Complex Numbers

Working with complex numbers in C enables mathematical and engineering applications requiring imaginary unit operations and polar coordinates. Create structures storing real and imaginary components: struct complex { double real, imag; }. Implement addition, subtraction, multiplication, and division operations handling both components correctly. Complex number arithmetic appears in signal processing, electrical engineering, and physics simulations. This project demonstrates practical mathematical programming and structured data manipulation for scientific computing applications.

#include <complex.h>
#include <stdio.h>

int main() {
    // Create complex numbers
    double complex z1 = 3.0 + 4.0*I;
    double complex z2 = 1.0 - 2.0*I;
    
    printf("z1 = %.1f + %.1fi\n", creal(z1), cimag(z1));
    printf("z2 = %.1f + %.1fi\n", creal(z2), cimag(z2));
    
    // Basic operations
    double complex sum = z1 + z2;
    double complex product = z1 * z2;
    
    printf("Sum: %.1f + %.1fi\n", creal(sum), cimag(sum));
    printf("Product: %.1f + %.1fi\n", creal(product), cimag(product));
    
    return 0;
}

🔹 Complex Functions

Mathematical functions for complex numbers including magnitude, argument, square root, and exponential enable advanced calculations in scientific applications. The C99 standard provides complex.h with built-in complex number support and mathematical functions. Calculate magnitude using the Pythagorean theorem on components and argument using arctangent. Implement or use library functions for roots and exponentials handling complex arithmetic correctly. These advanced functions enable implementation of signal processing algorithms, Fourier transforms, and quantum mechanical simulations requiring complex number operations.

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

int main() {
    double complex z = 1.0 + 1.0*I;
    
    // Magnitude and argument
    double magnitude = cabs(z);
    double argument = carg(z);
    
    printf("z = %.2f + %.2fi\n", creal(z), cimag(z));
    printf("Magnitude: %.3f\n", magnitude);
    printf("Argument: %.3f radians\n", argument);
    
    // Complex functions
    double complex sqrt_z = csqrt(z);
    double complex exp_z = cexp(z);
    double complex log_z = clog(z);
    
    printf("sqrt(z) = %.3f + %.3fi\n", creal(sqrt_z), cimag(sqrt_z));
    printf("exp(z) = %.3f + %.3fi\n", creal(exp_z), cimag(exp_z));
    printf("log(z) = %.3f + %.3fi\n", creal(log_z), cimag(log_z));
    
    return 0;
}