# Complex numbers in C++ | Set 2

• Difficulty Level : Basic
• 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

 `// 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)`

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

 `// 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)```

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

 `// 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)```

Time Complexity: O(1)

Auxiliary Space: O(1)

This article is contributed by Shambhavi Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes arrow_drop_up