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

$$ \begin{aligned} -\frac{4}{5}-5i &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]-5\cdot\frac{4}{5}-5\cdot5i &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]-4-25i &= 0&& \text{ move the constants to the right } \\[1 em]-25i &= 4&& \text{ divide both sides by $ -25 $ } \\[1 em]i &= -\frac{4}{25}&& \\[1 em] \end{aligned} $$

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