$$ \begin{aligned} \frac{12093}{1000} &= \frac{95}{100}+\frac{195}{100}i+i^2&& \text{multiply ALL terms by } \color{blue}{ 1000 }. \\[1 em]1000\cdot\frac{12093}{1000} &= 1000\cdot\frac{95}{100}+1000\frac{195}{100}i+1000i^2&& \text{cancel out the denominators} \\[1 em]12093 &= 950+1950i+1000i^2&& \text{simplify right side} \\[1 em]12093 &= 950+1950i-1000&& \\[1 em]12093 &= 1950i-50&& \text{ swap the left and right side of the equation } \\[1 em]1950i-50 &= 12093&& \text{ move -50 to the right } \\[1 em]1950i &= 12093+50&& \\[1 em]1950i &= 12143&& \text{ divide both sides by $ 1950 $ } \\[1 em]i &= \frac{12143}{1950}&& \\[1 em] \end{aligned} $$

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