Question

(\frac{2 - 4i}{3i})

Explanation:

Step1: Multiply numerator and denominator by \(i\) to rationalize the denominator.

\(\frac{2 - 4i}{3i} \times \frac{i}{i}=\frac{(2 - 4i)i}{3i\times i}\)

Step2: Expand the numerator and simplify the denominator.

Numerator: \((2 - 4i)i = 2i-4i^{2}\), and since \(i^{2}=- 1\), it becomes \(2i + 4\).
Denominator: \(3i\times i=3i^{2}=-3\).
So we have \(\frac{4 + 2i}{-3}\)

Step3: Split the fraction.

\(\frac{4 + 2i}{-3}=-\frac{4}{3}-\frac{2}{3}i\)

Answer:

\(-\frac{4}{3}-\frac{2}{3}i\)