$$-\frac{4}{5}-2i = 0$$

$$ \begin{aligned} -\frac{4}{5}-2i &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]-5\cdot\frac{4}{5}-5\cdot2i &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]-4-10i &= 0&& \text{ move the constants to the right } \\[1 em]-10i &= 4&& \text{ divide both sides by $ -10 $ } \\[1 em]i &= -\frac{4}{10}&& \\[1 em]i &= -\frac{2}{5}&& \\[1 em] \end{aligned} $$

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