Question

Simplify : i^17

Answer 1

take the integer remainder when dividing 17 by 4
since 17 = 4*4+1 the remainder is 1
therefore \(i^{17}=i^1=i\)

Answer 2

i^17 = i(i^16) = i[(i^2)^8) = i[(-1)^8] = i(1)=i

Answer 3

pattern is
\[i^0=1,i^1=i,i^2=-1,i^3=-i, i^4=1 ...\]

Answer 4

cool thanks guys!