Complex numbers in C++ | Set 2

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           // for std::complex, std::log #include   using namespace std;     // driver program int main () {       // initializing the complex: (-1.0+0.0i)   complex mycomplex (-1.0, 0.0);       // use of log()   cout << "The log of " << mycomplex << " is "        << log(mycomplex) <

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           // CPP program to illustrate // std::complex, std::cos, std::sin, std::tan #include   using namespace std;     // driver program int main () {       // initializing the complex: (-1.0+0.0i)   complex mycomplex (0.0, 1.0);       // use of cos()   cout << "The cos of " << mycomplex << " is "        << cos(mycomplex) <

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 #include    // For std::complex #include using namespace std;     // Driver program int main() {            // behaves like real cosh, sinh, tanh along the real line;     // z = a + 0i     complex z(1, 0);      cout << "cosh" << z << " = " << cosh(z)               << " (cosh(1) = " << cosh(1) << ")"< z2(0, 1);      cout << "cosh" << z2 << " = " << cosh(z2)               << " ( cos(1) = " << cos(1) << ")"<

/div>

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)