`complex` 類別

文章
10/12/2023

類別範本描述一個物件，該物件會儲存類型 Type為的兩個物件，一個代表複數的實際部分，另一個代表虛數部分。

語法

template <class Type>
class complex

備註

類別 Type的物件：

具有公用預設建構函式、解構函式、複製建構函式和指派運算子，且這些都具有傳統行為。
可指派整數或浮點值，或轉換類型為具有傳統行為的值。
可視需要定義算術運算子和數學函式，將其定義為具有傳統行為的浮點類型。

特別是在指派之後，細微的差異可能不存在於複製建構和預設建構之間。類別對 Type 象上沒有任何作業可能會擲回例外狀況。

類別範本 complex 的明確特製化存在三個浮點類型。在此實作中，任何其他型 Type 別的值都是針對實際計算進行型別轉換 double ， double 結果會指派回類型的 Type預存物件。

成員

建構函式

名稱	描述
`complex`	建構具有指定實數與虛數部分或作為其他一些複數複本的複數。

Typedefs

名稱	描述
`value_type`	類型，表示用來代表複數之實數和虛數部分的資料類型。

函式

名稱	描述
`imag`	擷取複數的虛數部分。
`real`	擷取複數的實數部分。

操作員

名稱	描述
`operator*=`	將目標複數乘以某個因數，該因數可能是複雜類型，或者是與複數的實數和虛數部分相同的類型。
`operator+=`	將數位加入目標複數，其中新增的數位可能很複雜，或與所加入複數的實數和虛數部分相同。
`operator-=`	從目標複數減去一個數位，其中減去的數位可能是複數，或與所加入複數的實數和虛數部分相同。
`operator/=`	將目標複數除以某個除數，該除數可能是複雜類型，或者是與複數的實數和虛數部分相同的類型。
`operator=`	將數位指派給目標複數，其中指派的數位可能很複雜，或與指派的複數的實數和虛數部分相同。

`complex`

建構具有指定實數與虛數部分或作為其他一些複數複本的複數。

constexpr complex(
    const T& _RealVal = 0,
    const T& _ImagVal = 0);

template <class Other>
constexpr complex(
    const complex<Other>& complexNum);

參數

_RealVal
用於初始化建構中複數之實數部分的值。

_ImagVal
用於初始化建構中複數之虛數部分的值。

complexNum
其實數及虛數用於初始化建構中之複數的複數。

備註

第一個建構函式會將預存的實數部分初始化為 _RealVal ，並將預存的虛數部分初始化為 _Imagval。第二個建構函式會將預存的實數部分初始化為 complexNum.real() ，並將儲存的虛數部分初始化為 complexNum.imag()。

在此實作中，如果翻譯工具不支援成員範本函式，則範本：

template <class Other>
complex(const complex<Other>& right);

取代為：

complex(const complex& right);

此為複製建構函式。

範例

// complex_complex.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
    using namespace std;
    double pi = 3.14159265359;

    // The first constructor specifies real & imaginary parts
    complex<double> c1( 4.0 , 5.0 );
    cout << "Specifying initial real & imaginary parts,"
        << "c1 = " << c1 << endl;

    // The second constructor initializes values of the real &
    // imaginary parts using those of another complex number
    complex<double> c2( c1 );
    cout << "Initializing with the real and imaginary parts of c1,"
        << " c2 = " << c2 << endl;

    // Complex numbers can be initialized in polar form
    // but will be stored in Cartesian form
    complex<double> c3( polar( sqrt( (double)8 ) , pi / 4 ) );
    cout << "c3 = polar( sqrt( 8 ) , pi / 4 ) = " << c3 << endl;

    // The modulus and argument of a complex number can be recovered
    double absc3 = abs( c3 );
    double argc3 = arg( c3 );
    cout << "The modulus of c3 is recovered from c3 using: abs( c3 ) = "
        << absc3 << endl;
    cout << "Argument of c3 is recovered from c3 using:\n arg( c3 ) = "
        << argc3 << " radians, which is " << argc3 * 180 / pi
        << " degrees." << endl;
}

`imag`

擷取複數的虛數部分。

T imag() const;

T imag(const T& right);

參數

right
要擷取其虛數部分的複數。

傳回值

複數的虛數部分。

備註

若為複數 a + bi，虛數部分或分量為 Im(a + bi) = b。

範例

// complex_imag.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
    using namespace std;

    complex<double> c1( 4.0 , 3.0 );
    cout << "The complex number c1 = " << c1 << endl;

    double dr1 = c1.real();
    cout << "The real part of c1 is c1.real() = "
        << dr1 << "." << endl;

    double di1 = c1.imag();
    cout << "The imaginary part of c1 is c1.imag() = "
        << di1 << "." << endl;
}

The complex number c1 = (4,3)
The real part of c1 is c1.real() = 4.
The imaginary part of c1 is c1.imag() = 3.

`operator*=`

將目標複數乘以某個因數，該因數可能是複雜類型，或者是與複數的實數和虛數部分相同的類型。

template <class Other>
complex& operator*=(const complex<Other>& right);

complex<Type>& operator*=(const Type& right);

complex<Type>& operator*=(const complex<Type>& right);

參數

right
複數或與目標複數之參數相同類型的數字。

傳回值

複數，其已乘以指定的參數數字。

備註

系統會將運算多載以執行簡單的算數運算，而無須將資料轉換成特定格式。

範例

// complex_op_me.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main()
{
    using namespace std;
    double pi = 3.14159265359;

    // Example of the first member function
    // type complex<double> multiplied by type complex<double>
    complex<double> cl1( polar ( 3.0 , pi / 6 ) );
    complex<double> cr1( polar ( 2.0 , pi / 3 ) );
    cout << "The left-side complex number is cl1 = " << cl1 << endl;
    cout << "The right-side complex number is cr1 = " << cr1 << endl;

    complex<double> cs1 = cl1 * cr1;
    cout << "Quotient of two complex numbers is: cs1 = cl1 * cr1 = "
        << cs1 << endl;

    // This is equivalent to the following operation
    cl1 *= cr1;
    cout << "Quotient of two complex numbers is also: cl1 *= cr1 = "
        << cl1 << endl;

    double abscl1 = abs ( cl1 );
    double argcl1 = arg ( cl1 );
    cout << "The modulus of cl1 is: " << abscl1 << endl;
    cout << "The argument of cl1 is: "<< argcl1 << " radians, which is "
        << argcl1 * 180 / pi << " degrees." << endl << endl;

    // Example of the second member function
    // type complex<double> multiplied by type double
    complex<double> cl2 ( polar ( 3.0 , pi / 6 ) );
    double cr2 = 5.0;
    cout << "The left-side complex number is cl2 = " << cl2 << endl;
    cout << "The right-side complex number is cr2 = " << cr2 << endl;

    complex<double> cs2 = cl2 * cr2;
    cout << "Quotient of two complex numbers is: cs2 = cl2 * cr2 = "
        << cs2 << endl;

    // This is equivalent to the following operation
    cl2 *= cr2;
    cout << "Quotient of two complex numbers is also: cl2 *= cr2 = "
        << cl2 << endl;

    double abscl2 = abs ( cl2 );
    double argcl2 = arg ( cl2 );
    cout << "The modulus of cl2 is: " << abscl2 << endl;
    cout << "The argument of cl2 is: "<< argcl2 << " radians, which is "
        << argcl2 * 180 / pi << " degrees." << endl;
}

`operator+=`

將數位加入目標複數，其中新增的數位可能很複雜，或與所加入複數的實數和虛數部分相同。

template <class Other>
complex<Type>& operator+=(const complex<Other>& right);

complex<Type>& operator+=(const Type& right);

complex<Type>& operator+=(const complex<Type>& right);

參數

right
複數或與目標複數之參數相同類型的數字。

傳回值

複數，其已加上指定的參數數字。

備註

系統會將運算多載以執行簡單的算數運算，而無須將資料轉換成特定格式。

範例

// complex_op_pe.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Example of the first member function
   // type complex<double> added to type complex<double>
   complex<double> cl1( 3.0 , 4.0 );
   complex<double> cr1( 2.0 , -1.0 );
   cout << "The left-side complex number is cl1 = " << cl1 << endl;
   cout << "The right-side complex number is cr1 = " << cr1 << endl;

   complex<double> cs1 = cl1 + cr1;
   cout << "The sum of the two complex numbers is: cs1 = cl1 + cr1 = "
        << cs1 << endl;

   // This is equivalent to the following operation
   cl1 += cr1;
   cout << "The complex number cr1 added to the complex number cl1 is:"
        << "\n cl1 += cr1 = " << cl1 << endl;

   double abscl1 = abs( cl1 );
   double argcl1 = arg( cl1 );
   cout << "The modulus of cl1 is: " << abscl1 << endl;
   cout << "The argument of cl1 is: "<< argcl1 << " radians, which is "
        << argcl1 * 180 / pi << " degrees." << endl << endl;

   // Example of the second member function
   // type double added to type complex<double>
   complex<double> cl2( -2 , 4 );
   double cr2 =5.0;
   cout << "The left-side complex number is cl2 = " << cl2 << endl;
   cout << "The right-side complex number is cr2 = " << cr2 << endl;

   complex<double> cs2 = cl2 + cr2;
   cout << "The sum of the two complex numbers is: cs2 = cl2 + cr2 = "
        << cs2 << endl;

   // This is equivalent to the following operation
   cl2 += cr2;
   cout << "The complex number cr2 added to the complex number cl2 is:"
        << "\n cl2 += cr2 = " << cl2 << endl;

   double abscl2 = abs( cl2 );
   double argcl2 = arg( cl2 );
   cout << "The modulus of cl2 is: " << abscl2 << endl;
   cout << "The argument of cl2 is: "<< argcl2 << " radians, which is "
        << argcl2 * 180 / pi << " degrees." << endl << endl;
}

The left-side complex number is cl1 = (3,4)
The right-side complex number is cr1 = (2,-1)
The sum of the two complex numbers is: cs1 = cl1 + cr1 = (5,3)
The complex number cr1 added to the complex number cl1 is:
cl1 += cr1 = (5,3)
The modulus of cl1 is: 5.83095
The argument of cl1 is: 0.54042 radians, which is 30.9638 degrees.

The left-side complex number is cl2 = (-2,4)
The right-side complex number is cr2 = 5
The sum of the two complex numbers is: cs2 = cl2 + cr2 = (3,4)
The complex number cr2 added to the complex number cl2 is:
cl2 += cr2 = (3,4)
The modulus of cl2 is: 5
The argument of cl2 is: 0.927295 radians, which is 53.1301 degrees.

`operator-=`

從目標複數減去一個數位，其中減去的數位可能是複數，或與所加入複數的實數和虛數部分相同。

template <class Other>
complex<Type>& operator-=(const complex<Other>& complexNum);

complex<Type>& operator-=(const Type& _RealPart);

complex<Type>& operator-=(const complex<Type>& complexNum);

參數

complexNum
複數，其為目標複數的減數。

_RealPart
實數，其為目標複數的減數。

傳回值

複數，其已減去指定的參數數字。

備註

系統會將運算多載以執行簡單的算數運算，而無須將資料轉換成特定格式。

範例

// complex_op_se.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Example of the first member function
   // type complex<double> subtracted from type complex<double>
   complex<double> cl1( 3.0 , 4.0 );
   complex<double> cr1( 2.0 , -1.0 );
   cout << "The left-side complex number is cl1 = " << cl1 << endl;
   cout << "The right-side complex number is cr1 = " << cr1 << endl;

   complex<double> cs1 = cl1 - cr1;
   cout << "The difference between the two complex numbers is:"
        << "\n cs1 = cl1 - cr1 = " << cs1 << endl;

   // This is equivalent to the following operation
   cl1 -= cr1;
   cout << "Complex number cr1 subtracted from complex number cl1 is:"
        << "\n cl1 -= cr1 = " << cl1 << endl;

   double abscl1 = abs( cl1 );
   double argcl1 = arg( cl1 );
   cout << "The modulus of cl1 is: " << abscl1 << endl;
   cout << "The argument of cl1 is: "<< argcl1 << " radians, which is "
        << argcl1 * 180 / pi << " degrees." << endl << endl;

   // Example of the second member function
   // type double subtracted from type complex<double>
   complex<double> cl2( 2.0 , 4.0 );
   double cr2 = 5.0;
   cout << "The left-side complex number is cl2 = " << cl2 << endl;
   cout << "The right-side complex number is cr2 = " << cr2 << endl;

   complex<double> cs2 = cl2 - cr2;
   cout << "The difference between the two complex numbers is:"
        << "\n cs2 = cl2 - cr2 = " << cs2 << endl;

   // This is equivalent to the following operation
   cl2  -= cr2;
   cout << "Complex number cr2 subtracted from complex number cl2 is:"
        << "\n cl2 -= cr2 = " << cl2 << endl;

   double abscl2 = abs( cl2 );
   double argcl2 = arg( cl2 );
   cout << "The modulus of cl2 is: " << abscl2 << endl;
   cout << "The argument of cl2 is: "<< argcl2 << " radians, which is "
        << argcl2 * 180 / pi << " degrees." << endl << endl;
}

The left-side complex number is cl1 = (3,4)
The right-side complex number is cr1 = (2,-1)
The difference between the two complex numbers is:
cs1 = cl1 - cr1 = (1,5)
Complex number cr1 subtracted from complex number cl1 is:
cl1 -= cr1 = (1,5)
The modulus of cl1 is: 5.09902
The argument of cl1 is: 1.3734 radians, which is 78.6901 degrees.

The left-side complex number is cl2 = (2,4)
The right-side complex number is cr2 = 5
The difference between the two complex numbers is:
cs2 = cl2 - cr2 = (-3,4)
Complex number cr2 subtracted from complex number cl2 is:
cl2 -= cr2 = (-3,4)
The modulus of cl2 is: 5
The argument of cl2 is: 2.2143 radians, which is 126.87 degrees.

`operator/=`

將目標複數除以某個除數，該除數可能是複雜類型，或者是與複數的實數和虛數部分相同的類型。

template <class Other>
complex<Type>& operator/=(const complex<Other>& complexNum);

complex<Type>& operator/=(const Type& _RealPart);

complex<Type>& operator/=(const complex<Type>& complexNum);

參數

complexNum
複數，其為目標複數的減數。

_RealPart
實數，其為目標複數的減數。

傳回值

複數，其已除以指定的參數數字。

備註

系統會將運算多載以執行簡單的算數運算，而無須將資料轉換成特定格式。

範例

// complex_op_de.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Example of the first member function
   // type complex<double> divided by type complex<double>
   complex<double> cl1( polar (3.0 , pi / 6 ) );
   complex<double> cr1( polar (2.0 , pi / 3 ) );
   cout << "The left-side complex number is cl1 = " << cl1 << endl;
   cout << "The right-side complex number is cr1 = " << cr1 << endl;

   complex<double> cs1 = cl1 / cr1;
   cout << "The quotient of the two complex numbers is: cs1 = cl1 /cr1 = "
        << cs1 << endl;

   // This is equivalent to the following operation
   cl1 /= cr1;
   cout << "Quotient of two complex numbers is also: cl1 /= cr1 = "
        << cl1 << endl;

   double abscl1 = abs( cl1 );
   double argcl1 = arg( cl1 );
   cout << "The modulus of cl1 is: " << abscl1 << endl;
   cout << "The argument of cl1 is: "<< argcl1 << " radians, which is "
        << argcl1 * 180 / pi << " degrees." << endl << endl;

   // Example of the second member function
   // type complex<double> divided by type double
   complex<double> cl2( polar(3.0 , pi / 6 ) );
   double cr2 =5;
   cout << "The left-side complex number is cl2 = " << cl2 << endl;
   cout << "The right-side complex number is cr2 = " << cr2 << endl;

   complex<double> cs2 = cl2 / cr2;
   cout << "The quotient of the two complex numbers is: cs2 /= cl2 cr2 = "
        << cs2 << endl;

   // This is equivalent to the following operation
   cl2 /= cr2;
   cout << "Quotient of two complex numbers is also: cl2 = /cr2 = "
        << cl2 << endl;

   double abscl2 = abs( cl2 );
   double argcl2 = arg( cl2 );
   cout << "The modulus of cl2 is: " << abscl2 << endl;
   cout << "The argument of cl2 is: "<< argcl2 << " radians, which is "
        << argcl2 * 180 / pi << " degrees." << endl << endl;
}

The left-side complex number is cl1 = (2.59808,1.5)
The right-side complex number is cr1 = (1,1.73205)
The quotient of the two complex numbers is: cs1 = cl1 /cr1 = (1.29904,-0.75)
Quotient of two complex numbers is also: cl1 /= cr1 = (1.29904,-0.75)
The modulus of cl1 is: 1.5
The argument of cl1 is: -0.523599 radians, which is -30 degrees.

The left-side complex number is cl2 = (2.59808,1.5)
The right-side complex number is cr2 = 5
The quotient of the two complex numbers is: cs2 /= cl2 cr2 = (0.519615,0.3)
Quotient of two complex numbers is also: cl2 = /cr2 = (0.519615,0.3)
The modulus of cl2 is: 0.6
The argument of cl2 is: 0.523599 radians, which is 30 degrees.

`operator=`

將數位指派給目標複數，其中指派的數位可能很複雜，或與指派的複數的實數和虛數部分相同。

template <class Other>
complex<Type>& operator=(const complex<Other>& right);

complex<Type>& operator=(const Type& right);

參數

right
複數或與目標複數之參數相同類型的數字。

傳回值

複數，其已指派指定的參數數字。

備註

系統會將運算多載以執行簡單的算數運算，而無須將資料轉換成特定格式。

範例

// complex_op_as.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Example of the first member function
   // type complex<double> assigned to type complex<double>
   complex<double> cl1( 3.0 , 4.0 );
   complex<double> cr1( 2.0 , -1.0 );
   cout << "The left-side complex number is cl1 = " << cl1 << endl;
   cout << "The right-side complex number is cr1 = " << cr1 << endl;

   cl1  = cr1;
   cout << "The complex number cr1 assigned to the complex number cl1 is:"
        << "\ncl1 = cr1 = " << cl1 << endl;

   // Example of the second member function
   // type double assigned to type complex<double>
   complex<double> cl2( -2 , 4 );
   double cr2 =5.0;
   cout << "The left-side complex number is cl2 = " << cl2 << endl;
   cout << "The right-side complex number is cr2 = " << cr2 << endl;

   cl2 = cr2;
   cout << "The complex number cr2 assigned to the complex number cl2 is:"
        << "\ncl2 = cr2 = " << cl2 << endl;

   cl2 = complex<double>(3.0, 4.0);
   cout << "The complex number (3, 4) assigned to the complex number cl2 is:"
        << "\ncl2 = " << cl2 << endl;
}

The left-side complex number is cl1 = (3,4)
The right-side complex number is cr1 = (2,-1)
The complex number cr1 assigned to the complex number cl1 is:
cl1 = cr1 = (2,-1)
The left-side complex number is cl2 = (-2,4)
The right-side complex number is cr2 = 5
The complex number cr2 assigned to the complex number cl2 is:
cl2 = cr2 = (5,0)
The complex number (3, 4) assigned to the complex number cl2 is:
cl2 = (3,4)

`real`

取得或設定 real 複數的元件。

constexpr T real() const;

T real(const T& right);

參數

right
要擷取其 real 值的複數。

傳回值

real複數的一部分。

備註

對於複數 a + bi，元件 real 或元件為 Re（a + bi） = a。

範例

// complex_class_real.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;

   complex<double> c1( 4.0 , 3.0 );
   cout << "The complex number c1 = " << c1 << endl;

   double dr1 = c1.real();
   cout << "The real part of c1 is c1.real() = "
        << dr1 << "." << endl;

   double di1 = c1.imag();
   cout << "The imaginary part of c1 is c1.imag() = "
        << di1 << "." << endl;
}

The complex number c1 = (4,3)
The real part of c1 is c1.real() = 4.
The imaginary part of c1 is c1.imag() = 3.

`value_type`

類型，表示用來代表複數之實數和虛數部分的資料類型。

typedef Type value_type;

備註

value_type 是類別複雜 Type 範本參數的同義字。

範例

// complex_valuetype.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
    using namespace std;
    complex<double>::value_type a = 3, b = 4;

    complex<double> c1 ( a , b );
    cout << "Specifying initial real & imaginary parts"
        << "\nof type value_type: "
        << "c1 = " << c1 << "." << endl;
}

Specifying initial real & imaginary parts
of type value_type: c1 = (3,4).

另請參閱

C++ 標準程式庫中的執行緒安全

分享方式：

complex 類別

語法

備註

成員

建構函式

Typedefs

函式

操作員

complex

參數

備註

範例

imag

參數

傳回值

備註

範例

operator*=

參數

傳回值

備註

範例

operator+=

參數

傳回值

備註

範例

operator-=

參數

傳回值

備註

範例

operator/=

參數

傳回值

備註

範例

operator=

參數

傳回值

備註

範例

real

參數

傳回值

備註

範例

value_type

備註

範例

另請參閱

意見反映

更多資源

`complex` 類別

`complex`

`imag`

`operator*=`

`operator+=`

`operator-=`

`operator/=`

`operator=`

`real`

`value_type`