Question

Divide:$\frac{2+4i}{5i}$

Short answer

The solution of the above expression is$\frac{4-2i}{5}$

Step-by-step solution

Given information

We are given an expression$\frac{2+4i}{5i}$

Write denominator in standard form

We get,$\frac{2+4i}{0+5i}$

 Multiply the numerator and denominator byThe complex conjugate of the denominator.

$\frac{2+4i}{0+5i}\times \frac{0-5i}{0-5i}$

Multiply and simplify the real and imaginary terms

$$\begin{gathered} \frac{-10i-20i^2}{-25i^2} \\ \frac{-10i-20(-1)}{-25(-1)} \\ \frac{20-10i}{25} \end{gathered}$$

Rewrite in standard form

$$\begin{gathered} \frac{20}{25}-\frac{10}{25}i \\ \frac{4}{5}-\frac{2}{5}i \end{gathered}$$

Conclusion

On solving the and performing the given operation we get$\frac{4}{5}-\frac{2}{5}i$