Chapter 2: Q15P (page 74)

Evaluate each of the following in $x + i y$ form, and compare with a computer solution. ${(- 1)}^{s i n i}$

Short Answer

Expert verified

The value of ${(- 1)}^{\sin i}$ is $e^{[- \sinh (1) (π \pm 2 n π)]}$ Where. $n = 0, 1, 2, 3, ...$

Step by step solution

Given Information.

The given expression is. ${(- 1)}^{\sin i}$

Definition of Complex Number and Hyperbolic functions.

The numbers that are presented in the form of $x + i y$ where, $x$ isthe real numbers and $y$ is an imaginary number, those numbers are referred to as called Complex numbers.

The basic hyperbolic functions are:

Hyperbolic sine(sinh)
Hyperbolic cosine(cosh)
Hyperbolic tangent(tanh)

Find the value of.(−1)sini

It is known that $\sin (i) = i \sinh (1)$

$\begin{matrix} {(- 1)}^{i \sinh (1)} = e^{(\ln ({(- 1)}^{i \sin (1)}))} \\ = e^{(i \sinh (1) \ln (- 1))} \\ = e^{[i \sinh (1) (\ln (1) + i (π \pm 2 n π))]} \\ {(- 1)}^{i \sinh (1)} = e^{[- \sinh (1) (π \pm 2 n π)]} \end{matrix}$

Hence,

The value of ${(- 1)}^{\sin i}$ is $e^{[- \sinh (1) (π \pm 2 n π)]}$ Where $n = 0, 1, 2, 3, ...$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Evaluate each of the following in $x + i y$ form, and compare with a computer solution. ${(- 1)}^{s i n i}$

Short Answer

Step by step solution

Given Information.

Definition of Complex Number and Hyperbolic functions.

Find the value of.(−1)sini

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Waves Physics

Work Energy and Power

Geometrical and Physical Optics

Famous Physicists

Translational Dynamics

Study anywhere. Anytime. Across all devices.

Evaluate each of the following inx+iy form, and compare with a computer solution.(−1)sini

Short Answer

Step by step solution

Given Information.

Definition of Complex Number and Hyperbolic functions.

Find the value of.(−1)sini

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Waves Physics

Work Energy and Power

Geometrical and Physical Optics

Famous Physicists

Translational Dynamics

Study anywhere. Anytime. Across all devices.

Evaluate each of the following in $x + i y$ form, and compare with a computer solution. ${(- 1)}^{s i n i}$