Divide

Divide.  (6i)/(5-4i)=  ?

$$\small{\text{ $ \dfrac{6i}{5-4i} \times \dfrac{5+4i}{5+4i} $ }}$\\\\$\small{\text{ $ = \dfrac{6i*(5+4i)}{(5-4i)(5+4i)} $ }}$\\\\$\small{\text{ $ = \dfrac{30i+24i^2}{25-16i^2} \quad \boxed{ i^2 = -1 } $ }}$\\\\$\small{\text{ $ = \dfrac{30i-24}{25+16} $ }}$\\\\$\small{\text{ $ = \dfrac{30i-24}{41} $ }}$\\\\$\small{\text{ $ = -\dfrac{24}{41} + \dfrac{30}{41}i $ }}$$

$$\\\frac{(6i)}{(5-4i)}\times \frac{(5+4i)}{(5+4i)}\\\\ =\frac{6i(5+4i)}{25--16}\\\\ =\frac{30i-24}{41}\\\\ =\frac{-24}{41}+\frac{30}{41}\;i$$

A small error has been repaired :)