Finding a negative power of $i$ How to find the value of $i$ when it has negative power? When solving for $i$ with positive power, I use something like
$$i^{101} = (i^{2})^{50}\times i = (-1)^{50} \times i = 1 \times i = i.$$
But how to solve for negative power of $i$ such as $i^{-10}$?
Can anyone explain what to do in this case?

Solution attempt:
I will solve for $i^{-3}$ as
$$i^{-3} = \frac{1}{i^3} = \frac{1}{i^2 \times i} = \frac{1}{-1 \times i} = \frac {1}{-i},$$
so the answer we get is $\dfrac{1}{-i}$. But my book is saying that I should get $i$.

By your analogy, $$i^{-10}=\frac{1}{i^{10}}=\frac{1}{i^8*i^2}=\frac{1}{(i^{2})^4* i^2}.$$ Since $i^2=-1$, it follows that $$i^{-10}=\frac{1}{(-1)^4*-1}=\frac{1}{-1}=-1.$$
