Question
$$\frac{1}{i} = -i$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} \frac{1}{i} &= -i&& \text{multiply ALL terms by } \color{blue}{ i }. \\[1 em]i\cdot\frac{1}{i} &= -ii&& \text{cancel out the denominators} \\[1 em]1 &= -i^2&& \text{move all terms to the left hand side } \\[1 em]1+i^2 &= 0&& \text{simplify left side} \\[1 em]1-1 &= 0&& \text{simplify left side} \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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