Difference between revisions of "Reciprocal of i"
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Latest revision as of 03:35, 8 December 2016
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.
