The complex library implements the complex class to contain complex numbers in cartesian form and several functions and overloads to operate with them.
- real() – It returns the real part of the complex number.
- imag() – It returns the imaginary part of the complex number.
// Program illustrating the use of real() and
// imag() function
#include <iostream>
// for std::complex, std::real, std::imag
#include <complex>
using
namespace
std;
// driver function
int
main()
{
// defines the complex number: (10 + 2i)
std::complex<
double
> 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;
}
Output:
Real part: 10 Imaginary part: 2
- abs() – It returns the absolute of the complex number.
- arg() – It returns the argument of the complex number.
// Program illustrating the use of arg() and abs()
#include <iostream>
// for std::complex, std::abs, std::atg
#include <complex>
using
namespace
std;
// driver function
int
main ()
{
// defines the complex number: (3.0+4.0i)
std::complex<
double
> 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;
}
Output:
The absolute value of (3,4) is: 5 The argument of (3,4) is: 0.927295
- polar() – It constructs a complex number from magnitude and phase angle.
real = magnitude*cosine(phase angle)
imaginary = magnitude*sine(phase angle)// Program illustrating the use of polar()
#include <iostream>
// std::complex, std::polar
#include <complex>
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;
}
Output:
The complex whose magnitude is 2 and phase angle is 0.5 is (1.75517,0.958851)
- norm() – It is used to find the norm(absolute value) of the complex number. If z = x + iy is a complex number with real part x and imaginary part y, the complex conjugate of z is defined as z'(z bar) = x – iy, and the absolute value, also called the norm, of z is defined as :
// example to illustrate the use of norm()
#include <iostream>
// for std::complex, std::norm
#include <complex>
using
namespace
std;
// driver function
int
main ()
{
// initializing the complex: (3.0+4.0i)
std::complex<
double
> mycomplex (3.0, 4.0);
// use of norm()
cout <<
"The norm of "
<< mycomplex <<
" is "
<< norm(mycomplex) <<endl;
return
0;
}
Output:
The norm of (3,4) is 25.
- conj() – It returns the conjugate of the complex number x. The conjugate of a complex number (real,imag) is (real,-imag).
// Illustrating the use of conj()
#include <iostream>
using
namespace
std;
// std::complex, std::conj
#include <complex>
// driver program
int
main ()
{
std::complex<
double
> mycomplex (10.0,2.0);
cout <<
"The conjugate of "
<< mycomplex <<
" is: "
;
// use of conj()
cout << conj(mycomplex) << endl;
return
0;
}
Output:
The conjugate of (10,2) is (10,-2)
- proj() – It returns the projection of z(complex number) onto the Riemann sphere. The projection of z is z, except for complex infinities, which are mapped to the complex value with a real component of INFINITY and an imaginary component of 0.0 or -0.0 (where supported), depending on the sign of the imaginary component of z.
// Illustrating the use of proj()
#include <iostream>
using
namespace
std;
// For std::complex, std::proj
#include <complex>
// driver program
int
main()
{
std::complex<
double
> c1(1, 2);
cout <<
"proj"
<< c1 <<
" = "
<< proj(c1) << endl;
std::complex<
double
> c2(INFINITY, -1);
cout <<
"proj"
<< c2 <<
" = "
<< proj(c2) << endl;
std::complex<
double
> c3(0, -INFINITY);
cout <<
"proj"
<< c3 <<
" = "
<< proj(c3) << endl;
}
Output:
proj(1,2) = (1,2) proj(inf,-1) = (inf,-0) proj(0,-inf) = (inf,-0)
- sqrt() – Returns the square root of x using the principal branch, whose cuts are along the negative real axis.
// Illustrating the use of sqrt()
#include <iostream>
using
namespace
std;
// For std::ccomplex, stdc::sqrt
#include <complex>
// driver program
int
main()
{
// use of sqrt()
cout <<
"Square root of -4 is "
<<
sqrt
(std::complex<
double
>(-4, 0)) << endl
<<
"Square root of (-4,-0), the other side of the cut, is "
<<
sqrt
(std::complex<
double
>(-4, -0.0)) << endl;
}
Output:
Square root of -4 is (0,2) Square root of (-4,-0), the other side of the cut, is (0,-2)
Next article: Complex numbers in C++ | Set 2
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- norm() – It is used to find the norm(absolute value) of the complex number. If z = x + iy is a complex number with real part x and imaginary part y, the complex conjugate of z is defined as z'(z bar) = x – iy, and the absolute value, also called the norm, of z is defined as :
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