Question

Simplify. i^-7 .

Answer 1

Well,
\[ i^{-7} = \frac{1}{i^7} \]
What first is
\[ i^7 = ... \]

Answer 2

which is -i

Answer 3

correct. Now what is 1/(-i)

Answer 4

oh wait. I think i know what i did wrong. its cause i forgot that i cannot be on the bottom of the equation. just to make sure. I believe the answer is i?

Answer 5

Yes, because you simplify complex fractions by multiplying by the conjugate of the denominator
\[ \frac{1}{-i} = \frac{1}{-i}\frac{i}{i} = \frac{i}{1} = i \]

Answer 6

thx.