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 $\frac{3}{\sqrt{2}} (1 - i)$ .

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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.

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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

Engineering Physics

Physical Quantities And Units

Geometrical and Physical Optics

Circular Motion and Gravitation

Wave Optics

Electric Charge Field and Potential

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.
$e^{- (i π / 4) + \ln 3}$ .