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. 

• 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)

• 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)

• 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)