Question

Can anyone show me whats up with this number?

Answer 1

\[i^-55\]

Answer 2

thats supose to be raised to the -55

Answer 3

is it
\[i^{-55}\]?

Answer 4

yea sorry i messed up in the equation maker

Answer 5

so that means
\[\frac{1}{i^{55}}\]right?

Answer 6

Yes but i think i'm supose to get it to equal 1 somehow

Answer 7

and
\[i^{55}\] is easy enough to compute because it goes
\[i^0=1,i^1=i,i^2=-1,i^3=-i, i^4=1,...\]

Answer 8

so i^-55=i?

Answer 9

so just take the whole number remainder when you divide 55 by 4, and see what you get. it is 3, since 4 goes in to 52 evenly
therefore
\[i^{55}=i^3=-i\]

Answer 10

and so
\[\frac{1}{i^{55}}=\frac{1}{-i}=\frac{1}{-i}\times \frac{i}{i}=\frac{i}{1}=i\]

Answer 11

probably a snappier way to do it, but yes it is i

Answer 12

but it is not 1, that is for sure

Answer 13

Ok so it's kinda like raising a negitive number to a power if the power is even the number is even, but instead if the power is odd it equals i or if it's even it equals 1?