Question

Simplify i^23

Answer 1

1

–1

–i

i

Answer 2

i

Answer 3

let's take a smaller number say i^5

i^5=i*i*i*i*i
=-1*-1*i
=i

So since it is i^23 it must be equal to i

Answer 4

Although I love answering questions on here, this link can help you a lot.
http://www.wolframalpha.com/input/?i=i%5E23

Answer 5

my apologies it DoodleTech is right.

i^23=-1*-1*-1*-1*-1*-1*-1*-1*-1*-1*-1*i
=-1*i
= -i

Please disregard my example, does not work in this case.

Answer 6

all you need to is take the integer remainder when you divide the exponent by 4.
so for example the remainder when you divide 23 by 4 is 3, and therefore
\[i^{23}=i^3==i\]

Answer 7

That's what I forgot thanks satellite73