Answer:
-1
Step-by-step explanation:
so "i" is the square root of -1 (√-1). We know that i² = (√-1)², and that when we square a square root we end back up with whatever is inside of the square root.
This is why i² = -1
We can find a pattern from writing out a few exponents:
i¹ = i
i² = -1
i³ = -i [(-1)(i)]
i⁴ = 1 [-1 · -1]
------
i⁵ = i [(1)(i)]
i⁶ = -1 [(i)(i)]
i⁷ = -i [(-1)(i)]
i⁸ = 1 [(-i)(i)= -(i²)= -(-1) = 1]
------
i⁹ = i [1 · i]
we can see that the pattern of i repeats every 4 numbers, so by dividing 26 by 4 (and finding the remainder), we can figure out which step of the pattern we are on
26 / 4 = 6 [remainder of 2]
we know that there is a remainder of 2, meaning that we are on the "second step" in the pattern: -1
you can do the same thing for any number
hope this helps!!
Answer:
-1
Step-by-step explanation:
4 goes into 26 6 times, and then there's 2 remainder, so it's the same thing as i², which is -1
hope this is helpful :)
