Q29P - Mathematical Methods in Physical Sciences

Question

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

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

Step-by-Step Solution

Answer

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

Step 1: Given Information.

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

Step 2: 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)

Step 3: Write c o s h ( 2 π i ) in the form of ( x + i y ) .

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 $1+0i=1$.