Question

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

$\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{h}\mathbf{(}\mathit{i}\mathit{\pi }\mathbf{+}\mathbf{2}\mathbf{)}$

Short answer

The x + iy form of the given equation$cosh(i\pi +2)$ is -3.76 .

Step-by-step solution

Given Information.

The given expression is$cosh(i\pi +2)\mathrm{i}$ .

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form of x + iy in which x is the real part and y is the imaginary part.

Write in the form of x + iy .

Use the formula cosh(x + y) = cosh xcoshy+ sinh xsinh yto break the given question.

Let us suppose.

x =2

y =$\pi$

cosh(x + y) =coshxcoshy+ sinhxsinhy

Put the values.

$$\begin{gathered} \cos h\left(i\pi +2\right)\mathrm{i}=\cosh \left(2\right)\cos \left(\pi \right)+i\sinh \left(2\right)\sin \pi \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}=-3.76 \end{gathered}$$

Therefore, the x + iy form of the given equation$\cos h\left(i\pi +2\right)\mathrm{i}$ is -3.76.