Question

Find the power of i. \[i ^{71}\]

Answer 1

This one is solved by the repeating pattern of powers of i. Recall\[i=\sqrt{-1}\implies i^2=-1\implies i^3=-i \implies i^4=1\implies i^5=i\]So.....\[i ^{71}=i ^{68}i^3=(i^4)^{17}i^3=i^3=-i\]

Answer 2

divide 71 by 4, the remainder is the equivalent expression
71/4=17 with a remainder of 3.
so equivalent expression is i^3 or -i

Answer 3

Since i^4=1, raising it to the seventeenth power is still one.

Answer 4

ooohh, alright. thank you guys. i'll try one of those answers. :)