Question

Divide, writing the answer in standard form: $\frac{-2}{-1+2i}$

Short answer

The solution of the above equation is $\frac{2}{5}+\frac{4}{5}i$

Step-by-step solution

Given information

We are given an equation$\frac{-2}{-1+2i}$

Multiply the numerator and denominator by thecomplex conjugate of the denominator.

$\frac{-2}{-1+2i}\times \frac{-1-2i}{-1-2i}$

Multiply in the numerator and use the Product ofComplex Conjugates Pattern in the denominator.

$\frac{-2(-1-2i)}{1-4i^2}$

Simplify 

$$\begin{gathered} \frac{2+4i}{1-4(-1)} \\ \frac{2+4i}{1+4} \\ \frac{2+4i}{5} \end{gathered}$$

 Write in standard form 

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

Conclusion

The solution of the above equation is$\frac{2}{5}+\frac{4}{5}i$