Chapter 2: Q12P (page 74)

Evaluate each of the following in $x + iy$ form, and compare with a computer solution.
role="math" localid="1658810193292" ${(i)}^{3 + i}$

Short Answer

Expert verified

The $x + iy$ form of the given equation $i^{(3 + i)}$ is, $- i e^{(- \frac{π}{2} \bar{+} 2 n π)}$

Step by step solution

Given Information.

The given expression is ${(i)}^{3 + i}$ .

Meaning of rectangular form.

Represent 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.

Convert in rectangular form.

Consider, $w = i^{(3 + i)}$ .

Write the given number in polar form.

$w = e^{[(3 + i) In (i)]}$

Use the logarithm property.

$w = e^{[(3 + i) In (i)]} w = e^{[(3 + i) (In (1) + i (\frac{π}{2} \bar{+} 2 nπ)]} w = e^{[(3 + i) i (\frac{π}{2} + 2 nπ)]} w = e^{(- \frac{π}{2} \bar{+} 2 n π + i (\frac{3 π}{2} + 6 nπ))} w = e^{(- \frac{π}{2} \bar{+} 2 n π)} e^{(i (\frac{3 π}{2} + 6 nπ))} w = - i e^{(- \frac{π}{2} \bar{+} 2 n π)}$

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

Therefore, $x = i y$ form of the given equation $i^{(3 + i)}$ is $- i e^{(\frac{π}{2} \bar{+} 2 n π)}$

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.

Evaluate each of the following in $x + iy$ form, and compare with a computer solution.
role="math" localid="1658810193292" ${(i)}^{3 + i}$

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Convert in rectangular form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Space Physics

Fields in Physics

Scientific Method Physics

Particle Model of Matter

Fluids

Study anywhere. Anytime. Across all devices.

Evaluate each of the following in x+iyform, and compare with a computer solution.role="math" localid="1658810193292" (i)3+i

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Convert in rectangular form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Space Physics

Fields in Physics

Scientific Method Physics

Particle Model of Matter

Fluids

Study anywhere. Anytime. Across all devices.

Evaluate each of the following in $x + iy$ form, and compare with a computer solution.
role="math" localid="1658810193292" ${(i)}^{3 + i}$