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--Division w. Complex Number Involvement

$\displaystyle \dfrac{8i}{4-3i}$

$\displaystyle \dfrac{8i}{4-3i} \times \dfrac{4+3i}{4+3i}$

$\displaystyle (4-3i)(4+3i) = 16+12i-12i-9(i^2) = 16+12i-12i-9(-1) = 16+9 = 25$

$\displaystyle (8i)(4+3i) = 32i-24$

$\displaystyle \dfrac{32i-24}{25}$

Standard Form: $\displaystyle -\dfrac{24}{25}+\dfrac{32}{25}i$