Question

How do you find what exponents of i are? like I know i^2 is -1, but how are you supposed to figure out i^26? do you have to write it all out?

THANK YOU

Answer 1

-1

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 :)

Answer 2

-1

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!!