Q35P - Mathematical Methods in Physical Sciences

Question

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

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

Step-by-Step Solution

Answer

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

Step 1: Given Information.

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

Step 2: 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.

Step 3: Write in the form of x + iy .

Use the formula cosh(x + y) = cosh x cosh y + sinh x sinh y to break the given question.

 

Let us suppose.

             x =2

             y =$\pi$

cosh(x + y) =cosh x cosh y + sinh x sinh y 

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.