C++中的复数|套装1

复杂库实现了复杂类，以包含笛卡尔形式的复数以及用于对其进行操作的若干函数和重载。

• real() –返回复数的实数部分。
• imag() –返回复数的虚部。

  // Program illustrating the use of real() and 
  // imag() function
  #include      
    
  // for std::complex, std::real, std::imag
  #include       
  using namespace std;
    
  // driver function
  int main()
  {    
    // defines the complex number: (10 + 2i)
    std::complex mycomplex(10.0, 2.0);
    
    // prints the real part using the real function
    cout << "Real part: " << real(mycomplex) << endl;
    cout << "Imaginary part: " << imag(mycomplex) << endl;
    return 0;
  }
  

  输出：

  Real part: 10
  Imaginary part: 2
  

• abs() –返回复数的绝对值。
• arg() –返回复数的参数。

  // Program illustrating the use of arg() and abs()
  #include      
    
  // for std::complex, std::abs, std::atg
  #include  
  using namespace std;
    
  // driver function
  int main ()
  {    
    // defines the complex number: (3.0+4.0i)
    std::complex mycomplex (3.0, 4.0);
    
    // prints the absolute value of the complex number
    cout << "The absolute value of " << mycomplex << " is: ";
    cout << abs(mycomplex) << endl;
      
    // prints the argument of the complex number
    cout << "The argument of " << mycomplex << " is: ";
    cout << arg(mycomplex) << endl;
    
    return 0;
  }
  

  输出：

  The absolute value of (3,4) is: 5
  The argument of (3,4) is: 0.927295
  

• polar() –它从幅度和相位角度构造一个复数。

  实=幅度*余弦(相角)
  虚数=大小*正弦(相角)

  // Program illustrating the use of polar()
  #include      
    
  // std::complex, std::polar
  #include 
  using namespace std;
    
  // driver function
  int main ()
  {
    cout << "The complex whose magnitude is " << 2.0;
    cout << " and phase angle is " << 0.5;
      
    // use of polar()
    cout << " is " << polar (2.0, 0.5) << endl;
    
    return 0;
  }
  

  输出：

  The complex whose magnitude is 2 and phase angle is 0.5 is (1.75517,0.958851)
  

• norm() –用于查找复数的范数(绝对值)。如果z = x + iy是具有实部x和虚部y的复数，则z的复共轭定义为z’(z bar)= x – iy，并且z的绝对值(也称为范数)定义为：
  

  // example to illustrate the use of norm()
  #include      
    
  // for std::complex, std::norm
  #include  
  using namespace std;
    
  // driver function
  int main ()
  {    
    // initializing the complex: (3.0+4.0i)
    std::complex mycomplex (3.0, 4.0);
    
    // use of norm()
    cout << "The norm of " << mycomplex << " is " 
         << norm(mycomplex) <

  输出：

  The norm of (3,4) is 25.
  

• conj() –返回复数x的共轭。复数(real，imag)的共轭是(real，-imag)。

  // Illustrating the use of conj()
  #include  
  using namespace std;
    
  // std::complex, std::conj
  #include       
    
  // driver program
  int main ()
  {
    std::complex mycomplex (10.0,2.0);
    
    cout << "The conjugate of " << mycomplex << " is: ";
      
    // use of conj()
    cout << conj(mycomplex) << endl;
    return 0;
  }
  

  输出：

  The conjugate of (10,2) is (10,-2)
  

• proj() –返回z(复数)在黎曼球面上的投影。 z的投影为z，除复数无穷外，根据z虚数分量的符号，复数无限性映射到具有INFINITY的实数分量和虚数分量为0.0或-0.0(在支持的情况下)的复数值。

  // Illustrating the use of proj()
    
  #include 
  using namespace std;
    
  // For std::complex, std::proj
  #include 
     
  // driver program
  int main()
  {
      std::complex c1(1, 2);
      cout << "proj" << c1 << " = " << proj(c1) << endl;
     
      std::complex c2(INFINITY, -1);
      cout << "proj" << c2 << " = " << proj(c2) << endl;
     
      std::complex c3(0, -INFINITY);
      cout << "proj" << c3 << " = " << proj(c3) << endl;
  }
  

  输出：

  proj(1,2) = (1,2)
  proj(inf,-1) = (inf,-0)
  proj(0,-inf) = (inf,-0)
  

• sqrt() –使用主体分支返回x的平方根，该主体的切割沿负实轴。

  // Illustrating the use of sqrt()
  #include 
  using namespace std;
    
  // For std::ccomplex, stdc::sqrt
  #include 
     
  // driver program
  int main()
  {    
      // use of sqrt()
      cout << "Square root of -4 is "
           << sqrt(std::complex(-4, 0)) << endl
           << "Square root of (-4,-0), the other side of the cut, is "
           << sqrt(std::complex(-4, -0.0)) << endl;
  }
  

  输出：

  Square root of -4 is (0,2)
  Square root of (-4,-0), the other side of the cut, is (0,-2)
  

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