step 1
Determine the complex conjugate of the denominator
the complex conjugate of the denominator is (6-4i)
step 2
Multiply the numerator and denominator of the fraction by the complex conjugate of the denominator
we have
[tex]\frac{2-5i}{6+4i}\cdot\frac{6-4i}{6-4i}[/tex]
Multiply
[tex]\frac{2-5i}{6+4i}\cdot\frac{6-4i}{6-4i}=\frac{(12-8i-30i+20i^2)}{36-16i^2}[/tex]
Remmeber that
i^2=-1
substitute
[tex]\begin{gathered} \frac{(12-8i-30i-20)}{36+16} \\ \\ \frac{-8-38i}{52} \\ \\ -\frac{8}{52}-\frac{38}{52}i \end{gathered}[/tex]
Simplify
[tex]-\frac{2}{13}-\frac{19}{26}i[/tex]
