Question

i^18

Answer 1

i^18 = 1i^2 = -1

Answer 2

divide 18 by 4, take the integer remainder. you get 2 because
\[18=4\times 16+2\] then write
\[i^{18}=i^2=-1\]

Answer 3

i, -1, -i, 1 is the pattern it goes in. divisible by 4 = 1, divisible by 2 but not 4 = -1

Answer 4

i^4=1
i^18=i^(4(4)+2)
i^4(4)xi^2
1x(-1)
=-1