Chapter 2: Q10P (page 69)

Find each of the following in rectangular form $x + i y$ and check your results by computer. Remember to save time by doing as much as you can in your head.
$s i n (i In i)$ .

Short Answer

Expert verified

The rectangular form of the given question is, $s i n (i I n i) = - 1$ .

Step by step solution

Given Information.

The given expression is $\sin (i In i)$ .

Meaning of rectangular form.

Representing the complex number in rectangular form means writing the given complex number in the form of $x + i y$ , in which $x$ is the real part and $y$ is the imaginary part.

Step 3: Put the value in the formula.

Use the complex formula $\sin θ = \frac{e^{i θ} - e^{- i θ}}{2 i}$ to rewrite the above expression as,

$\sin (i In i) = \frac{e^{(i . i In i)} - e^{(- i . i In i)}}{2 i} \sin (i In i) = \frac{e^{(- In (i))} - e^{(In i)}}{2 i} = \frac{i^{- 1} - i}{2 i} = \frac{\frac{1}{i} - i}{2 i} = \frac{1 - i^{2}}{2 i} = \frac{1 + 1}{- 2} \sin (i In i) = - 1$

Therefore, the rectangular form of $\sin (i In i)$ is $- 1$ .

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Find each of the following in rectangular form $x + i y$ and check your results by computer. Remember to save time by doing as much as you can in your head.
$s i n (i In i)$ .

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Step 3: Put the value in the formula.

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Find each of the following in rectangular form x+iy and check your results by computer. Remember to save time by doing as much as you can in your head.sin(iIni) .

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Step 3: Put the value in the formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Quantum Physics

Physics of Motion

Fundamentals of Physics

Famous Physicists

Measurements

Study anywhere. Anytime. Across all devices.

Find each of the following in rectangular form $x + i y$ and check your results by computer. Remember to save time by doing as much as you can in your head.
$s i n (i In i)$ .