Solve the following equation :
$i x^{2} - x + 12 i = 0$

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Solution

We have,
$\begin{matrix} i x^{2} - x + 12 i = 0 i x^{2} - 4 x + 3 x + 12 i = 0 i x (x - \frac{4}{i}) + 3 (x + 4 i) = 0 i x (x - \frac{4}{i} \times \frac{i}{i}) + 3 (x + 4 i) = 0 i x (x - \frac{4 i}{i^{2}}) + 3 (x + 4 i) = 0 i x (x - \frac{4 i}{- 1}) + 3 (x + 4 i) = 0 i x (x + 4 i) + 3 (x + 4 i) = 0 (x + 4 i) (i x + 3) = 0 x = - 4 i, \frac{- 3}{i} \times \frac{i}{i} = - 3 i / i^{2} = 3 i S o, x = - 4 i, 3 i \end{matrix}$

Hence, this is the answer.

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