Reciprocal of i

From specialfunctionswiki
Revision as of 03:35, 8 December 2016 by Tom (talk | contribs) (Created page with "==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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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.

References