Question

I need help with this practice problem solving It asks to divide

Answer 1

`-(5)/(13)-(14i)/(13)`

Step-by-step explanation

We want to divide the given complex fraction:

`(4+i)/(-2+3i)`

To do this, we have to rationalize the denominator of the fraction by multiplying the given fraction by another fraction made up of the conjugate of the denominator of the given fraction:

`(4+i)/(-2+3i)\cdot(-2-3i)/(-2-3i)`

Simplifying this, we have:

`\begin{gathered} ((4+i)(-2-3i))/((-2+3i)(-2-3i)) \\ \Rightarrow(-8-12i-2i+3)/(4+6i-6i+9) \\ (-8+3-12i-2i)/(13)=(-5-14i)/(13) \\ \Rightarrow-(5)/(13)-(14i)/(13) \end{gathered}`

That is the solution of the division.