1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
umka21 [38]
3 years ago
10

Please Help!!Use Euler’s formula to write in exponential form.

Mathematics
1 answer:
LekaFEV [45]3 years ago
4 0

Answer:

C, 4e^{i(7\pi/4)}

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

e^{ix}=\cos{x}+i\sin{x}

Given the complex number 2\sqrt{2}-2i\sqrt{2}, we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.

One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression 2(\sqrt{2}-i\sqrt{2})

Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression 4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right) , and <em>now </em>we have something to work with.

Looking back at Euler's formula e^{ix}=\cos{x}+i\sin{x}, we can map our expression inside the parentheses to the one on the right side of the formula, giving us \cos{x}=\frac{\sqrt2}{2} and \sin{x}=-\frac{\sqrt2}{2}, or equivalently:

\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x

At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so x=\frac{7\pi}{4}, and we can finally replace our expression in parentheses with its exponential equivalent:

4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}

Which is c on the multiple choice section.

You might be interested in
What’s 5 equivalent ratios to 27:9
Feliz [49]

3:1

6:2

24:8

15:5

30:10

hope this helps, have a great day :)

8 0
3 years ago
Read 2 more answers
17. Critique Reasoning Lisa used a number line to model 2(3). Does her number line make sense? Explain why or why not. 8-7-6-5-4
timama [110]

Reasoning Criticism Lisa modeled 2 with a number line (3). Her logical number line is -6.

<h3>What is meant by number line?</h3>
  • A number line is a graphical representation of numbers on a straight line. A number line has numbers that are sequentially placed at equal distances along its length.
  • It can be extended in any direction indefinitely and is usually represented horizontally. A number line is a horizontal line with mathematical increments spaced evenly.
  • The numbers on the line will determine how to answer the number on the line. The number's use is determined by the question that goes with it, such as plotting a point.
  • The number line is a straight line with divisions at equal intervals, similar to a scale.

Therefore, Reasoning Criticism Lisa modeled 2 with a number line (3). Her logical number line is -6.

To learn more about number line, refer to:

brainly.com/question/24644930

#SPJ1

8 0
1 year ago
Please help! I will mark as brainliest. &lt;3
Verdich [7]

Answer:

7

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
which number has one digit that represents 10 times the value of the digit to it's right? 375,595, 545,150 and 378,658
Artyom0805 [142]

It would be 375,595.

3 0
3 years ago
Read 2 more answers
Which of the following ordered pairs does not represent a dependent relationship?
cricket20 [7]

It is D, not here because they are all dependent.
6 0
3 years ago
Read 2 more answers
Other questions:
  • 51,487 rounded by nearest thousand
    5·1 answer
  • WHOEVER GETS IT RIGHT GETS BRAINLIEST
    9·1 answer
  • Can someone do this quickly please?
    15·2 answers
  • 10,13,16,19<br> What is the 30th term?
    8·1 answer
  • What is the missing side length of the right triangle ? 8in and 15in
    9·1 answer
  • What are two different statistics that demographers use to study population? define the statistics?
    11·2 answers
  • Gustavo tested 1000 calculators to see if any were defective. The company claimed that the probability of a defective calculator
    13·3 answers
  • Does anyone know this?
    15·1 answer
  • What is the area of this trapezoid?
    14·1 answer
  • What are two variables that might be positively related to academic success?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!