# 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<``double``> 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<``double``> 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<``double``> z(1, 0);  ` `    ``cout << ``"cosh"` `<< z << ``" = "` `<< ``cosh``(z) ` `              ``<< ``" (cosh(1) = "` `<< ``cosh``(1) << ``")"``< z2(0, 1);  ` `    ``cout << ``"cosh"` `<< z2 << ``" = "` `<< ``cosh``(z2) ` `              ``<< ``" ( cos(1) = "` `<< ``cos``(1) << ``")"``<

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)
```

## tags:

C++ CPP-Library cpp-numerics-library CPP