# C 语言标准库头文件 complex.h

#include <stdio.h>
#include <complex.h>  // 复数支持
#include <math.h>     // 数学函数

int main(void) {
    // ========== 1. 复数基础操作 ==========
    double complex z1 = 3.0 + 4.0 * I;  // 3 + 4i
    double complex z2 = 1.0 - 2.0 * I;  // 1 - 2i

    // 算术运算
    double complex sum = z1 + z2;
    double complex product = z1 * z2;
    double complex conjugate = conj(z1);

    printf("基础运算:\n");
    printf("z1 + z2 = %.2f %+.2fi\n", creal(sum), cimag(sum));
    printf("z1 * z2 = %.2f %+.2fi\n", creal(product), cimag(product));
    printf("z1的共轭复数 = %.2f %+.2fi\n\n", creal(conjugate), cimag(conjugate));

    // ========== 2. 工程应用：阻抗计算 ==========
    double R = 5.0;    // 电阻 (Ω)
    double L = 0.1;     // 电感 (H)
    double omega = 50;  // 角频率 (rad/s)
    double complex Z = R + omega * L * I;  // 阻抗 Z = R + jωL

    printf("阻抗计算 (RLC电路):\n");
    printf("Z = %.2f + j%.2f Ω\n", creal(Z), cimag(Z));
    printf("|Z| = %.2f Ω\n", cabs(Z));
    printf("Z 的相位角 = %.2f 度\n\n", carg(Z) * 180 / M_PI);

    // ========== 3. 信号处理：DFT计算 ==========
    double complex signal[] = {1 + 0*I, 0 + 1*I, -1 + 0*I, 0 - 1*I};  // 示例信号
    int N = sizeof(signal) / sizeof(signal[0]);
    double complex freq_component = 0;

    for (int k = 0; k < N; k++) {
        freq_component += signal[k] * cexp(-I * 2 * M_PI * k / N);  // DFT公式
    }

    printf("信号分析 (DFT):\n");
    printf("基频分量 = %.2f %+.2fi\n", creal(freq_component), cimag(freq_component));
    printf("幅值主值 = %.2f, 相位 = %.2f°\n\n", 
           cabs(freq_component), carg(freq_component) * 180 / M_PI);

    // ========== 4. 复数函数应用 ==========
    double complex z = 1.0 + 1.0 * I;
    printf("复数函数:\n");
    printf("e^(1+i) = %.2f %+.2fi\n", creal(cexp(z)), cimag(cexp(z)));
    printf("sqrt(i) = %.2f %+.2fi\n", creal(csqrt(I)), cimag(csqrt(I)));
    printf("sin(iπ/2) = %.2fi\n", cimag(csin(I * M_PI_2)));

    return 0;
}