Reciprocal of i

Theorem

The following formula holds: $$\dfrac{1}{i}=-i,$$ where $i$ denotes the imaginary number.

Proof

Using the fact that $\dfrac{i}{i}=1$ and the square of i, we see that $$\dfrac{1}{i} = \left( \dfrac{1}{i} \right) \left( \dfrac{i}{i} \right) = \dfrac{i}{i^2} = -i,$$ as was to be shown.