# How do you simplify (3+9i)/(3i)?

$\frac{3 + 9 i}{3 i} = \frac{\cancel{3} \left(1 + 3 i\right)}{\left(\cancel{3}\right) i} = \frac{1 + 3 i}{i} = \frac{1 + 3 i}{i} \times \frac{i}{i} = \frac{i + 3 {i}^{2}}{i} ^ 2 = \frac{i - 3}{-} 1 = 3 - i$.
Alternatively, $\frac{3 + 9 i}{3 i} = \frac{3}{3 i} + \frac{9 i}{3 i} = \frac{1}{i} + 3 = \left\{\frac{1 \cdot i}{i \cdot i}\right\} + 3$
$= \frac{i}{i} ^ 2 + 3 = \frac{i}{-} 1 + 3 = 3 - i$.