Chapter 2: Q3P (page 69)

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.
$e^{- (i π / 4) + \ln 3}$ .

Short Answer

Expert verified

The rectangular form of the given question is $e^{- (\frac{i π}{4}) + \ln 3} = \frac{3}{\sqrt{2}} (1 - i)$ .

Step by step solution

Given Information.

The given expression is $e^{- (i π / 4) + \ln 3} . .$

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.

Separate the exponential.

The given question is $e^{- (i π / 4) + \ln 3}$ .

Break the exponential part in the given question.

$e^{- (\frac{i π}{4}) + \ln 3} = e^{- (\frac{i π}{4})} e^{\ln 3} e^{- (\frac{i π}{4}) + \ln 3} = e^{- \frac{i π}{4}} \times 3 e^{- (\frac{i π}{4}) + \ln 3} = 3 e^{\frac{- i π}{4}}$

Convert it into rectangular form.

Use the complex formula $e^{- i θ} = \cos θ - i \sin θ$ to rewrite the above expression.

$3 e^{\frac{- i π}{4}} = 3 [\cos (\frac{π}{4}) - i \sin (\frac{π}{4})] = 3 (\frac{1}{\sqrt{2}} - i \frac{1}{\sqrt{2}}) = \frac{3}{\sqrt{2}} (1 - i)$

Therefore, the rectangular form of role="math" localid="1658737730577" $e^{- (i π / 4) + \ln 3}$ is $\frac{3}{\sqrt{2}} (1 - i)$ .

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 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.
$e^{- (i π / 4) + \ln 3}$ .

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Separate the exponential.

Convert it into rectangular form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Dynamics

Kinematics Physics

Measurements

Quantum Physics

Work Energy and Power

Study anywhere. Anytime. Across all devices.

Find each of the following in rectangular form x+iyand check your results by computer. Remember to save time by doing as much as you can in your head.e-(iπ/4)+ln3.

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Separate the exponential.

Convert it into rectangular form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Dynamics

Kinematics Physics

Measurements

Quantum Physics

Work Energy and Power

Study anywhere. Anytime. Across all devices.

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.
$e^{- (i π / 4) + \ln 3}$ .