Chapter 2: Q7MP (page 80)

Find one or more values of each of the following complex expressions and compare with a computer solution.
$(- i)'$

Short Answer

Expert verified

The value of $(- i)'$ is, $e^{- (\frac{π}{2} \pm 2 n π)}$ .

Step by step solution

Given Information

The given expression is, $(- i)'$ .

Definition of Complex Numbers

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

Use the logarithmic functions to obtain the result

Consider, $w = (- i)'$ .

Write the number in the form, $w = e^{i I n (- i)}$ . …. (1)

Use logarithmic functions to find the value of In $(- i)$ .

$I n (- i) = I n (r) + i (θ \pm 2 n π) n = 0, 1, 2, 3, . . . . .$

$= I n (1) + i (\frac{π}{2} \pm 2 n π) = i (\frac{π}{2} \pm 2 n π) . . . . . . . . (2)$

Put the value of In $(- i)$ in equation (1).

$w = e^{[i . i (\frac{π}{2} \pm 2 n π)]} w = e^{[- (\frac{π}{2} \pm 2 n π)]} n = 0, 1, 2, 3, . . . . . . .$

Hence the value of ${(- i)}^{i}$ is, $e^{- (\frac{π}{2} \pm 2 n π)}$ .

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.

Find one or more values of each of the following complex expressions and compare with a computer solution.
$(- i)'$

Short Answer

Step by step solution

Given Information

Definition of Complex Numbers

Use the logarithmic functions to obtain the result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Astrophysics

Fluids

Engineering Physics

Physical Quantities And Units

Work Energy and Power

Study anywhere. Anytime. Across all devices.

Find one or more values of each of the following complex expressions and compare with a computer solution.(-i)'

Short Answer

Step by step solution

Given Information

Definition of Complex Numbers

Use the logarithmic functions to obtain the result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Astrophysics

Fluids

Engineering Physics

Physical Quantities And Units

Work Energy and Power

Study anywhere. Anytime. Across all devices.

Find one or more values of each of the following complex expressions and compare with a computer solution.
$(- i)'$