Question

divide and express the result in standard form.
\frac{3i}{6 - 8i}
\frac{3i}{6 - 8i}=square
(simplify your answer. type your answer in the form a + bi. use integers or fractions in the expression.)

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by the conjugate of the denominator $6 + 8i$.
$\frac{3i}{6 - 8i}\times\frac{6 + 8i}{6 + 8i}$

Step2: Expand numerator and denominator

For numerator: $3i(6 + 8i)=18i+24i^{2}$. Since $i^{2}=- 1$, it becomes $18i+24\times(-1)=-24 + 18i$.
For denominator: $(6 - 8i)(6 + 8i)=6^{2}-(8i)^{2}=36-64i^{2}=36-64\times(-1)=36 + 64 = 100$.

Step3: Write in standard form

$\frac{-24 + 18i}{100}=-\frac{24}{100}+\frac{18}{100}i=-\frac{6}{25}+\frac{9}{50}i$

Answer:

$-\frac{6}{25}+\frac{9}{50}i$