Question

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

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

Short answer

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

Step-by-step solution

Given Information.

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

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.

Write in the form of x + iy.

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

It is known that role="math" localid="1658809612460" $\sin \left(zi\right)=i\sin h\left(z\right)$.

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 .