Complex numbers in C++ | Set 2
Last Updated :
31 Aug, 2022
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
#include <iostream>
#include <complex>
using namespace std;
int main ()
{
complex< double > mycomplex (-1.0, 0.0);
cout << "The log of " << mycomplex << " is "
<< log (mycomplex) <<endl;
return 0;
}
|
The log of (-1,0) is (0,3.14159)
Time Complexity: O(1)
Auxiliary Space: O(1)
- 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)
CPP
#include <iostream>
#include <complex>
using namespace std;
int main ()
{
complex< double > mycomplex (0.0, 1.0);
cout << "The cos of " << mycomplex << " is "
<< cos (mycomplex) <<endl;
cout << "The sin of " << mycomplex << " is "
<< sin (mycomplex) <<endl;
cout << "The tan of " << mycomplex << " is "
<< tan (mycomplex) <<endl;
return 0;
}
|
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)
Time Complexity: O(1)
Auxiliary Space: O(1)
- cosh() – It finds the hyperbolic 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 hyperbolic sine is:
sinh(z)=(e^z-e^(-z))/2.
- tanh() – It finds the hyperbolic tangent of the given complex.Mathematical function of hyperbolic tan is:
tanh(z)=(e^(2z)-1)/(e^(2z)+1)
CPP
#include <iostream>
#include <cmath>
#include <complex>
using namespace std;
int main()
{
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;
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;
}
|
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)
Time Complexity: O(1)
Auxiliary Space: O(1)
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