Question

Find each of the following in the x+iy form and check your answers by computer.

$\mathit{c}\mathit{o}\mathit{s}\mathit{h}\left(2\pi i\right)$

Short answer

$\cos h\left(2\pi i\right)$can be written in the form of 1+0i=1.

Step-by-step solution

Given Information.

The given expression is $\cos h\left(2\pi i\right)$.

Definition of Complex Numberand Hyperbolic functions.

The domain of a function refers to the range of values that can be plugged into it. This is the set of x values in a function like f (x) . The range of a function is the set of values that the function can take. This is the set of values that the function produces when we enter x value. The y values are what you're looking for.

The basic hyperbolic functions are:

1. Hyperbolic sine(sinh)
2. Hyperbolic cosine(cosh)
3. Hyperbolic tangent(tanh)

Write cosh(2πi) in the form of (x+iy) .

Let$u=\cos h\left(2\pi i\right)$$u=\cos h\left(2\pi i\right)$

It is known that

$$\begin{gathered} \cos h\left(xi\right)=\cos \left(x\right) \\ u=\cos \left(2x\right) \\ 1 \end{gathered}$$.

Hence, $\cos h\left(2\pi i\right)$ can be written in the form of $1+0i=1$.