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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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There are 28 Year 8 students going on the ski trip, out of the 45 students going. Write this proportion as a percentage. Give yo
alexdok [17]

Answer:

62.2%

Step-by-step explanation:

We are told in the question that:

The total number of students going = 45 students

The number of year 8 students going for the ski trip = 28 students

The proportion is :

28/45

Converting this proportion to a percentage.

28/45 × 100

= 0.6222222222222222 × 100

62.222222222%

Approximately to 1 decimal place is

62.2%

3 0
3 years ago
When 843219 to the power of 100 is multiplied out, what is the units digit
Nina [5.8K]

For this case we have the following expression:

843,219

When multiplying to the power of 100 we have:

843,219 * 100 = 843,219 * 10 ^ 2 = 84,321,900

We have to:

0: Unit

0: Ten

9: Hundred

1: One thousand unit

2: Ten thousand

3: One hundred thousand

4: Million unit

8: Ten million

Thus, the unit digit is 0.

Answer:

0

8 0
4 years ago
Checking granddaughter homework not very good with math
lara31 [8.8K]
No, the perimeter equals, 10.55 yd. Add all of the sides together.
4 0
3 years ago
The cost for 15 cases of oranges is $75. What is the cost for 1 case? *
postnew [5]

Answer:Ok I This question can be solved using a system of equation, which requires translating the above word problem into something that can be algebraically

Let O=oranges and  Let G=Grapefruit

5O +8G=235

3O + 2G=85

To solve, you must isolate one of the variables and then work from there. To do that multiply both sides of the bottom or second equation by four and then subtract the bottom equation from the top.

Which would look like this

5O +8G=235

12O + 8G= 340

Then subtract the bottom from the top to get this

-7O=-105

Solving for O we divide both sides by -7, and end up with O=15

Plugging that value back into one of our original equations to solve for G we get this

3(15) + 2G= 85

45 +2G=85

2G=40

G=20

So 1 case of each altogether would equal 15+20, or $35.

<h3>Hope this helps have a awesome night/day❤️✨</h3>

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Lesson Quiz 9-3 1. What are the solutions of each equation? Use a graph of the related function. a. x2 + 4 = 4 b. x2 + 16 = 0 c.
dedylja [7]

Answer:

soryyyyyyyyy

Step-by-step explanation:

soryyyyyyyyyy

8 0
3 years ago
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