Question

How do you simplify i^40

Answer 1

`√(-1) \ \ \ | (...)^(2) \\ \\ i^(2) = -1 \\ \\ i^(3) = √(-1)^(3) = ( √(-1))^(2)* √(-1) =-i \\ \\ i^(4)=(i^(2))^(2)=(-1)^(2)=1 \\ \\ i^(40) = (i^(4))^(10) = 1^(10) = 1`

==================================

"Associate with people who are likely to improve you."

Answer 2

well
i=√-1 so
i^2=(√-1)^2=-1
remember that
x^(mn)=(x^n)^m
i^40=(i^2)^20
we know that i^2=-1 so
i^40=-1^20
-1^2=1
-1^3=-1
-1^4=1
-1^5=-1
we conclude that even powers of -1 yeild +1 so the answer is +1 (positive 1)