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:
2
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Answer:
x = 3
Step-by-step explanation:
Because the endpoints of the segment with length 12.5 are the midpoints of the sides of the large trapezoid, the length of that segments, 12.5, is the average of the lengths of the top and bottom lengths of the large trapezoid.
(3x + 1 + 15)/2 = 12.5
Multiply both sides by 2.
3x + 16 = 25
3x = 9
x = 3
Answer:
Step-by-step explanation:
A linear equation looks like any other equation. It is made up of two expressions set equal to each other. A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction
