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.
Factored form: (x-5)(7x+5) ☺
Approx - 10%
72 students signed up for canoeing + the 23 students who signed up for trekking + the 13 students who signed up for both = 108 students
there are 120 students total, so you have to subtract 120 - 108 = 12
Now to find the percentage, you have to divide the number of students who didn't sign up for either, by the total
which is .1 = 10/100 = 10%
Answer:area is 150 cm
Step-by-step explanation:
