Q34P - Mathematical Methods in Physical Sciences

Question

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

$\mathit{s}\mathit{i}\mathit{n}\frac{\mathbf{i}\mathbf{\pi }}{\mathbf{2}}$

Step-by-Step Solution

Answer

The x + iy form of the given equation, $\sin \frac{i\pi }{2}$ is 2.3i .

Step 1: Given Information.

The given expression is $\sin \frac{i\pi }{2}$.

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 is the real part and is the imaginary part.

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

Let us suppose that $u=\sin \frac{i\pi }{2}$.

 

It is known that $\sin \left(zi\right)=i \sin h\left(z\right)$.

 

Substitute the value.

$$\begin{gathered} u=i \sin h\left(\frac{\pi }{2}\right) \\ =2.3 \end{gathered}$$

 

Therefore, the x + iy form of the given equation, $\sin \frac{i\pi }{2}$ is 2.31 i  .