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:
5.196152423
Step-by-step explanation:
Answer:
Page number 74
Step-by-step explanation:
Let
x ---> the number of days
y ---> the number of pages read
we know that
The linear equation in slope intercept form is equal to
where
m is the slope
b is the y-intercept
we have
<em>Anne</em>
The slope is equal to
The y-intercept is equal to
substitute
----> equation A
<em>Willow</em>
The slope is equal to
The y-intercept is equal to
substitute
----> equation B
equate equation A and equation B
solve for x
Find the value of y
substitute the value of x in equation A or equation B
equation A
equation B
Answer:
y = 7x + 15
Step-by-step explanation:
total cost = $7 x every hour + $15 renters fee
