$$ \begin{aligned} (7-3i)^2-(4i+1) &= 0&& \text{simplify left side} \\[1 em]49-42i+9i^2-(4i+1) &= 0&& \\[1 em]49-42i-9-(4i+1) &= 0&& \\[1 em]-42i+40-(4i+1) &= 0&& \\[1 em]-42i+40-4i-1 &= 0&& \\[1 em]-46i+39 &= 0&& \text{ move the constants to the right } \\[1 em]-46i &= -39&& \text{ divide both sides by $ -46 $ } \\[1 em]i &= \frac{-39}{-46}&& \\[1 em]i &= \frac{39}{46}&& \\[1 em] \end{aligned} $$

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