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Crazy boy [7]
4 years ago
11

Prove Euler's identity using Euler's formula. e^ix = cos x + i sin x

Mathematics
1 answer:
Korolek [52]4 years ago
3 0

First list all the terms out.

e^ix = 1 + ix/1! + (ix)^2/2! + (ix)^3/3! ...

Then, we can expand them.

e^ix = 1 + ix/1! + i^2x^2/2! + i^3x^3/3!...

Then, we can use the rules of raising i to a power.

e^ix = 1 + ix - x^2/2! - ix^3/3!...

Then, we can sort all the real and imaginary terms.

e^ix = (1 - x^2/2!...) + i(x - x^3/3!...)

We can simplify this.

e^ix = cos x + i sin x

This is Euler's Formula.

What happens if we put in pi?

x = pi

e^i*pi = cos(pi) + i sin(pi)

cos(pi) = -1

i sin(pi) = 0

e^i*pi = -1 OR e^i*pi + 1 = 0

That is Euler's identity.

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Solve for x and y<br>17) 2x - 3y = -1<br>y = x-1​
Cloud [144]

Answer:

x = 4 , y = 3

Step-by-step explanation:

Solve the following system:

{2 x - 3 y = -1 | (equation 1)

y = x - 1 | (equation 2)

Express the system in standard form:

{2 x - 3 y = -1 | (equation 1)

-x + y = -1 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{2 x - 3 y = -1 | (equation 1)

0 x - y/2 = (-3)/2 | (equation 2)

Multiply equation 2 by -2:

{2 x - 3 y = -1 | (equation 1)

0 x+y = 3 | (equation 2)

Add 3 × (equation 2) to equation 1:

{2 x+0 y = 8 | (equation 1)

0 x+y = 3 | (equation 2)

Divide equation 1 by 2:

{x+0 y = 4 | (equation 1)

0 x+y = 3 | (equation 2)

Collect results:

Answer: {x = 4 , y = 3

4 0
4 years ago
Which of the following shows the correct solution steps and solution to
Andreyy89

C.

3x + 2 = 17 \\ 3x + 2 - 2 = 17 - 2 \\  \:  \:  \:  \:  \:  \:  \:  \:  \: 3x = 15 \\ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  x =  \frac{15}{3}  \\  \:  \:  \:  \:  \:  \:  \:  \: x = 5

6 0
3 years ago
You have 20 quarters and then find 40% more and then spend 75% how much money do you have left
kirza4 [7]

You have $1.75 left

Step-by-step explanation:

Given,

Number of quarters already have = 20

Percent of quarters found = 40% of already have

Number of quarters found = \frac{40}{100}*20

Number of quarters found = \frac{800}{100}

Number of quarters found = 8

New total = 20+8 = 28 quarters

Percent of quarters spent = 75%

Number of quarters spent = \frac{75}{100}*28

Number of quarters spent = \frac{2100}{100}

Number of quarters spent = 21

Quarters left = 28-21 = 7

1 quarter = 25 cents

7 quarters = 25*7 = 175 cents

$1 = 100 cents

175 cents = \frac{175}{100}=\$1.75

You have $1.75 left

Keywords: division, addition

Learn more about division at:

  • brainly.com/question/2116906
  • brainly.com/question/2131336

#LearnwithBrainly

5 0
4 years ago
2) How many y pieces are in 6/12?
storchak [24]

Answer:

6 out of 12

Step-by-step explanation: there was 12 before but now there are 6 because probally somebody ate them

5 0
4 years ago
Write an equation of the line below.
sasho [114]
Here it is y=3/2x-2
3 0
3 years ago
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