c std ::複數示例

std::complex在C 中用於簡化複數運算，1. 需包含<complex>頭文件；2. 可用std::complex<double>(實部, 虛部)創建複數；3. 支持、-、*、/等基本運算；4. 通過real()和imag()訪問實虛部；5. 使用abs()求模，arg()求幅角，norm()求模平方；6. conj()返回共軛複數；7. exp()結合虛數單位可驗證歐拉公式；8. polar()函數可從極坐標創建複數。該模板避免手動實現複數運算，廣泛適用於數學、信號處理等領域。

Here's a practical example of using std::complex in C :

Basic Usage of std::complex

The std::complex template in C (from the <complex></complex> header) lets you work with complex numbers easily. Here's a simple example showing creation, arithmetic, and common operations:

 #include <iostream>
#include <complex>
#include <cmath>

int main() {
    // Create complex numbers
    std::complex<double> z1(3.0, 4.0); // 3 4i
    std::complex<double> z2(1.0, -2.0); // 1 - 2i

    // Output them
    std::cout << "z1 = " << z1 << std::endl; // Output: (3,4)
    std::cout << "z2 = " << z2 << std::endl; // Output: (1,-2)

    // Arithmetic operations
    std::cout << "z1 z2 = " << (z1 z2) << std::endl; // (4,2)
    std::cout << "z1 - z2 = " << (z1 - z2) << std::endl; // (2,6)
    std::cout << "z1 * z2 = " << (z1 * z2) << std::endl; // (11,-2)
    std::cout << "z1 / z2 = " << (z1 / z2) << std::endl; // (-1,2)

    // Access real and imaginary parts
    std::cout << "Re(z1) = " << z1.real() << std::endl; // 3
    std::cout << "Im(z1) = " << z1.imag() << std::endl; // 4

    // Magnitude and phase
    std::cout << "abs(z1) = " << std::abs(z1) << std::endl; // 5
    std::cout << "arg(z1) = " << std::arg(z1) << std::endl; // ~0.927 (radians)
    std::cout << "norm(z1) = " << std::norm(z1) << std::endl; // 25 (|z|²)

    // Complex conjugate
    std::cout << "conj(z1) = " << std::conj(z1) << std::endl; // (3,-4)

    // Euler&#39;s formula: e^(iπ) = -1
    std::complex<double> i(0, 1); // Imaginary unit
    std::complex<double> result = std::exp(i * M_PI);
    std::cout << "e^(i*pi) = " << result << std::endl; // Should be close to (-1,0)

    return 0;
}

Key Points

• Header : Always include <complex>
• Template types : Commonly std::complex<double> , but float and long double are also supported
• Construction : std::complex<double>(real, imag) or direct assignment like {a, b}
• Operators : , - , * , / work as expected
• Functions : std::abs , std::arg , std::conj , std::norm , std::exp , std::polar , etc.

Using polar form

You can also create complex numbers from magnitude and phase:

 double magnitude = 5.0;
double angle = M_PI / 3; // 60 degrees
std::complex<double> z_polar = std::polar(magnitude, angle);
std::cout << "Polar to rectangular: " << z_polar << std::endl;

This is especially useful in signal processing or physics simulations.

Basically, std::complex handles the math so you don't have to implement complex arithmetic manually — and it integrates well with standard math functions.

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