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
Crazy boy [7]
3 years ago
11

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

Mathematics
1 answer:
Korolek [52]3 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.

You might be interested in
Can you guys help me please
Setler79 [48]

Answer:   A And B

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
meriva
Add all the number then multiply by 1,000
8 0
3 years ago
Read 2 more answers
What is the answer 27x^3-1=0
chubhunter [2.5K]
X=cubic root 2/27
Glad to help
6 0
3 years ago
Read 2 more answers
PLEASE HELP WITH QUESTION C
GalinKa [24]

Answer:

Discount: 25%

Tax: 6.5%

Step-by-step explanation:

Percentage of discount:

x/100 = 10/39.99 (what percentage is 10 of 39.99) (%/100=is/of)

= 25%

Percentage of tax:

x/100 = 1.95/29.99

= 6.5%

8 0
3 years ago
Median for 35 45 26 32 46 38 39 40 26 72
zhenek [66]

Answer:

38.5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Polygon FFF has an area of 363636 square units. Aimar drew a scaled version of Polygon FFF and labeled it Polygon GGG. Polygon G
    12·1 answer
  • Two real-valued functions, f(x) and g(x), are defined as f(x) = x2 + 6x + 9 and g(x) = x2 – 9. Find the results of combining the
    14·2 answers
  • Determine the value of x for which a || b if m<30=80-x and m<7=90-2x.
    7·1 answer
  • Match the reasons with the statements in the proof.
    15·2 answers
  • By 3:00 pm, the temperature increased by another 5 degrees Fahrenheit was the temperature at 3:00pm positive or negative?
    15·1 answer
  • PLEASE HELP ME!! I WILL MARK BRAINIEST
    10·1 answer
  • Given that f(x) = 2x + 9, find the value that makes f(x) = 27.
    8·1 answer
  • Find the value of x ​
    15·1 answer
  • Allison read 4/8 of an hour everyday of the week. How many hours does she read each week
    14·2 answers
  • 2/5 × 6/7= simplify form​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!