Exponents!?

Question

i^2006

it is :
i to the 2006th power....!

i thought it was -2006 but its not! what is it then..?hm?

Answer 1

2006 divided by 4=501.5
501*4=2004
2006-2004=2
i^2=-1

i^2006=-1

Answer 2

powers of i go like this:

i^1 = i
i² = -1
i³ = -i
i^4 = 1......... and then repeat
so if we divide 2006 by 4, we get 501 r. 2, 2006 mod 4 = 2, so
i^2006 = i² = -1

somewhat more algebraically,
i^2006 = [(i^4)^501][i²] = [1^501][-1] = 1[-1] = -1

Answer 3

Go to google.com and type i^2006.
Press enter.
Google calculates the answer which is -1.

Answer 4

i^1=1 i^2=-1 i^3=-i i^4=1

2006 / 4 has remainder 2
so it is -1