anonymous 3 years ago Simplify. i^-7 .

1. JamesJ

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

2. anonymous

which is -i

3. JamesJ

correct. Now what is 1/(-i)

4. anonymous

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?

5. JamesJ

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

6. anonymous

thx.