Q37P - Mathematical Methods in Physical Sciences

Question

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

$\mathit{c}\mathbf{os}\mathbf{\left(}\mathbf{i}\mathbf{\pi }\mathbf{\right)}$

Step-by-Step Solution

Answer

The x+iy form of the given equation $\cos \left(i\pi \right)$ is 11.6.

Step 1: Given Information.

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

Step 2: Meaning of rectangular form.

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

Step 3: Write in the form of .

Let us suppose that, $u=\cos \left(i\pi \right)$.

 

It is known that, $\cos \left(xi\right)=\cosh \left(x\right)$.

 

Substitute the value.

$\begin{array}{l}u=\cosh \left(\mathrm{\pi }\right)\\ u=11.6\end{array}$

 

Therefore, the $x+iy$ form of the given equation is, $\cos \left(i\pi \right)$ is 11.6.