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 $n = 0, 1, 2, 3, ...$

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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

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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

Electricity and Magnetism

Electromagnetism

Scientific Method Physics

Energy Physics

Famous Physicists

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

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