Let's raise i to various powers starting with 0,1,2,3...
i^0 = 1
i^1 = i
i^2 = ( sqrt(-1) )^2 = -1
i^3 = i^2*i = -1*i = -i
i^4 = (i^2)^2 = (-1)^2 = 1
i^5 = i^4*i = 1*i = i
i^6 = i^5*i = i*i = i^2 = -1
We see that the pattern repeats itself after 4 iterations. The four items to memorize are
i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
It bounces back and forth between 1 and i, alternating in sign as well. This could be one way to memorize the pattern.
To figure out something like i^25, we simply divide the exponent 25 over 4 to get the remainder. In this case, the remainder of 25/4 is 1 since 24/4 = 6, and 25 is one higher than 24.
This means i^25 = i^1 = i
Likewise,
i^5689 = i^1 = i
because 5689/4 = 1422 remainder 1. The quotient doesn't play a role at all so you can ignore it entirely
Answer:
x=7/6
Step-by-step explanation:
subtract the 4x from both sides of the equation
(2x+6)-4x=4x-3-4x
find common denominator
(2x+6)/5+(5(-4)x)/5=4x-3-4x
then combine fractions
(2x+6+5(-4)x)/5=4x-3-4x
then multiply the 5&4
(2x+6-20x)/5= 4x3-4x
combine terms
(-18x+6)/5= -3
then multiply everything by 5
-18x+6= -15
subtract the 6 from both sides
-18x= -21
divide -21 by -18
(-21)/(-18)=x
find greatest common multiple (3) and solve
x = 7/6
Answer:
57
Step-by-step explanation:
9+6(2^2+4)
Calculate 2 to the power of 2 and get 4.
9+6(4+4)
Add 4 and 4 to get 8.
9+6×8
Multiply 6 and 8 to get 48.
9+48
Add 9 and 48 to get 57.
57
I think that the answer is 63 although I could be wrong
