Question

medal+fan.
Simplify i^22
A. 1

B. −1

C. −i

D. i

Answer 1

well we could split this up into small i^2 s because i^2 is equal to -1

Answer 2

I know I'm doing this the long way...
(i^2)(i^2)(i^2)(i^2)(i^2)(i^2)(i^2)(i^2)(i^2)(i^2)(i^2)
(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)
and then we find some pairs to make it faster.. I got 5 pairs of (-1)s

Answer 3

(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)
(1)(1)(1)(1)(-1) = -1

Answer 4

ok it is -1 and I figured out a shortcut.
we know that i^2 = -1
so we could modify the problem a bit
(i^2)^11
because 11 x 2 is 22 via distributive exponential rules
since i^2 = -1
(-1)^11 and we have an odd exponential so the result will be negative.... -1

Answer 5

B

Answer 6

i^1 = i

i^2= -1


i^3= -i

i^4= 1

i^5 = i

It repeats every 4