We introduced and discussed the concept in Complex numbers in C++ | Set 1
The remaining functions with example are discussed here:
- log() – It is used to return the log of the complex number.
// CPP program to illustrate the use of log()
#include <iostream>
// for std::complex, std::log
#include <complex>
using
namespace
std;
// driver program
int
main ()
{
// initializing the complex: (-1.0+0.0i)
complex<
double
> mycomplex (-1.0, 0.0);
// use of log()
cout <<
"The log of "
<< mycomplex <<
" is "
<<
log
(mycomplex) <<endl;
return
0;
}
Output:
The log of (-1,0) is (0,3.14159)
- cos() – It computes complex cosine of a complex value z. Mathematical definition of the cosine is
cos z = (e^(iz) + e^(-iz))/2
- sin() – It computes the complex sine of a complex value z. Mathematical definition of the cosine is
sin z = (e^(iz) - e^(-iz))/2i
- tan() – It computes the complex tangent of a complex value z. Mathematical definition of the tangent is
tan z = i(e^(-iz) - e^(iz)) / (e^(-iz) + e^iz)
// example to illustrate the use of sin(), cos() and tan()
#include <iostream>
// CPP program to illustrate
// std::complex, std::cos, std::sin, std::tan
#include <complex>
using
namespace
std;
// driver program
int
main ()
{
// initializing the complex: (-1.0+0.0i)
complex<
double
> mycomplex (0.0, 1.0);
// use of cos()
cout <<
"The cos of "
<< mycomplex <<
" is "
<<
cos
(mycomplex) <<endl;
// use of sin()
cout <<
"The sin of "
<< mycomplex <<
" is "
<<
sin
(mycomplex) <<endl;
// use of tan()
cout <<
"The tan of "
<< mycomplex <<
" is "
<<
tan
(mycomplex) <<endl;
return
0;
}
Output:
The cos of (0,1) is (1.54308,-0) The sin of (0,1) is (0,1.1752) The tan of (0,1) is (0,0.761594)
- cosh() – It finds the hyperolic cosine of the given complex. Mathematical function of hyperbolic cosine is:
cosh(z)=(e^z+e^(-z))/2
- sinh() – It finds the hyperbolic sine of the given complex. Mathematical function of hyperolic sine is:
sinh(z)=(e^z-e^(-z))/2.
- tanh() – It finds the hyperbolic tangent of the given complex.Mathematical function of hyperolic tan is:
tanh(z)=(e^(2z)-1)/(e^(2z)+1)
// CPP program to illustrate the
// use of cosh(),sinh(),tanh()
#include <iostream>
#include <cmath>
// For std::complex
#include <complex>
using
namespace
std;
// Driver program
int
main()
{
// behaves like real cosh, sinh, tanh along the real line;
// z = a + 0i
complex<
double
> z(1, 0);
cout <<
"cosh"
<< z <<
" = "
<<
cosh
(z)
<<
" (cosh(1) = "
<<
cosh
(1) <<
")"
<<endl;
cout <<
"sinh"
<< z <<
" = "
<<
sinh
(z)
<<
" (sinh(1) = "
<<
sinh
(1) <<
")"
<<endl;
cout <<
"tanh"
<< z <<
" = "
<<
tanh
(z)
<<
" (tanh(1) = "
<<
tanh
(1) <<
")"
<<endl;
// behaves like real cosine,sine,tangent along the imaginary line; z2=0+1i
complex<
double
> z2(0, 1);
cout <<
"cosh"
<< z2 <<
" = "
<<
cosh
(z2)
<<
" ( cos(1) = "
<<
cos
(1) <<
")"
<<endl;
cout <<
"sinh"
<< z2 <<
" = "
<<
sinh
(z2)
<<
" ( sin(1) = "
<<
sin
(1) <<
")"
<<endl;
cout <<
"tanh"
<< z2 <<
" = "
<<
tanh
(z2)
<<
" ( tan(1) = "
<<
tan
(1) <<
")"
<<endl;
}
Output:
cosh(1.000000,0.000000) = (1.543081,0.000000) (cosh(1) = 1.543081) sinh(1.000000,0.000000) = (1.175201,0.000000) (sinh(1) = 1.175201) tanh(1.000000,0.000000) = (0.761594,0.000000) (tanh(1) = 0.761594) cosh(0.000000,1.000000) = (0.540302,0.000000) ( cos(1) = 0.540302) sinh(0.000000,1.000000) = (0.000000,0.841471) ( sin(1) = 0.841471) tanh(0.000000,1.000000) = (0.000000,1.557408) ( tan(1) = 1.557408)
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