Question

i^23

Answer 1

-i

Answer 2

\[i^1=i\]\[i^2=-1\]\[i^3=-i\]\[i^4=1\]

Answer 3

assuming i is sqrt(-1)
we have i^2=-1
i^4=1
so break,i^23 as (i^4)^5*i^2*i
so what u get?

Answer 4

23 = ? (mod4)

Answer 5

I donot know this rule

Answer 6

i^23 = (i^4)^5 times (i^2) times i

Answer 7

i is an imaginary number that has a value of square root of negative 1

Answer 8

\[\sqrt{-1}\]

Answer 9

Anything to the 0th power is 1. Anything to the first power is itself. the definition of i squared is -1. i^3 is the same as i^2*i, and we alread know that i^2 is -1, so we know i^3=-i.

From there you can keep going, just expand i^power out into i*i*i*.... and put together negative 1s and you'll get there. But you might notice a pattern arises that alternates between the 4 different ones.

Answer 10

ohhh goti it so i ^23 is -1

Answer 11

but the answer is -i !!

Answer 12

yes

Answer 13

so what ever the power of i is at the end it is -1