$$ \begin{aligned} \frac{1}{i} &= i&& \text{multiply ALL terms by } \color{blue}{ i }. \\[1 em]i\cdot\frac{1}{i} &= ii&& \text{cancel out the denominators} \\[1 em]1 &= i^2&& \text{move all terms to the left hand side } \\[1 em]1-i^2 &= 0&& \text{simplify left side} \\[1 em]1+1 &= 0&& \text{simplify left side} \\[1 em]2 &= 0&& \\[1 em] \end{aligned} $$

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