# 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 <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 iscos z = (e^(iz) + e^(-iz))/2

**sin()**– It computes the complex sine of a complex value z. Mathematical definition of the cosine issin z = (e^(iz) - e^(-iz))/2i

**tan()**– It computes the complex tangent of a complex value z. Mathematical definition of the tangent istan 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)

This article is contributed by **Shambhavi Singh**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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