Question

Simplify.
i^38

Answer 1

\[i=\sqrt{-1}\]
\[i^{2}=-1\]
What value do you think even powers of i will have?

Answer 2

For example what is the value of\[i ^{4}\]

Answer 3

\[a^{mn}=(a^m)^n\]

Answer 4

No clue..

Answer 5

i^4 = 1

Answer 6

\[38 = 4*9 +2\]

\[i ^{38}=(i ^{4})^{9}*i^2\]

Answer 7

i^2 = -1

Answer 8

every 4 powers we have:
i,-1, -i, 1