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To use complex numbers involves these steps: 1 Create one or more complex objects The complex class is generic, and you must specify the type of the components This will normally be a floating-point type, such as double 2 Perform operations on complex objects by use of overloaded operators All of the arithmetic operators are defined for complex 3 Obtain the real component of a complex instance by calling real( ) 4 Obtain the imaginary component of a complex instance by calling imag( )
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Discussion
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The template specification for complex is shown here: template <class T> class complex Here, T specifies the type used to represent the components of a complex number There are three predefined specializations of complex: class complex< oat> class complex<double> class complex<long double> Specifying any other type argument is undefined The complex class has the following constructors: complex(const T &real = T( ), const T &imaginary = T( )) complex(const complex &ob) template <class T1> complex(const complex<T1> &ob); The first constructs a complex object with a real component of real and an imaginary component of imaginary These values default to zero if not specified The second creates a copy of ob The third creates a complex object from ob
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Herb Schildt's C++ Programming Cookbook
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The following operations are defined for complex objects:
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+ = = += == * /= != / *=
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The non-assignment operators are overloaded in three ways: once for operations involving a complex object on the left and a scalar object on the right, again for operations involving a scalar on the left and a complex object on the right, and finally for operations involving two complex objects For example, the following types of addition operations are allowed: complex_ob + scalar scalar + complex_ob complex_ob + complex_ob Two member functions are defined for complex: real( ) and imag( ) They are shown here: T real( ) const T imag( ) const The real( ) function returns the real component of the invoking object, and imag( ) returns the imaginary component The <complex> header also defines complex versions of the standard math functions, such as abs( ), sin( ), cos( ), and pow( )
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Example
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Here is a sample program that demonstrates complex:
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// Demonstrate the complex class #include <iostream> #include <complex> using namespace std; int main() { complex<double> cmpx1(1, 0); complex<double> cmpx2(1, 1); cout << "cmpx1: " << cmpx1 << endl << "cmpx2: " << cmpx2 << endl; // Add two complex numbers cout << "cmpx1 + cmpx2: " << cmpx1 + cmpx2 << endl;
7:
Potpourri
// Multiply two complex numbers cout << "cmpx1 * cmpx2: " << cmpx1 * cmpx2 << endl; // Add a scalar to a complex number cmpx1 += 20; cout << "cmpx1 += 20: " << cmpx1 << endl; // Find the sin of cmpx2 cout << "sin(cmpx2): " << sin(cmpx2) << endl; return 0; }
The output is shown here:
cmpx1: (1,0) cmpx2: (1,1) cmpx1 + cmpx2: (2,1) cmpx1 * cmpx2: (1,1) cmpx1 += 20: (3,0) sin(cmpx2): (129846,0634964)
Options and Alternatives
For programmers who focus on numeric computations, C++ provides more support than one might at first guess In addition to complex, C++ includes the valarray class that supports operations on numeric arrays It also supplies two utility classes called slice and gslice, which encapsulate a portion (ie, a slice) of an array These classes require the header <valarray> In the <numeric> header are defined four numeric algorithms called accumulate( ), adjacent_difference( ), inner_product( ), and partial_sum( ) All of these will be of interest to the numeric programmer
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Key Ingredients
Headers <memory> Classes auto_ptr Functions T *get( ) const throw( ) T *release( ) throw( ) void reset(X *ptr = 0) throw( )
C++ includes a class called auto_ptr that was designed to simplify the management of dynamically allocated memory As many readers will know, one of the most troubling
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