We have the following expression:
[tex]\frac{-2+i}{-4-5i}[/tex]
By multiplying this expression above and below by the complex conjugate of -4-5i , we have
[tex]\frac{-2+i}{-4-5i}=\frac{-2+i}{-4-5i}\times\frac{-4+5i}{-4+5i}[/tex]
which gives
[tex]\frac{-2+i}{-4-5i}=\frac{(-2+i)(-4+5i)}{16+25}=\frac{8-10i-4i-5}{16+25}[/tex]
which give us
[tex]\frac{-2+i}{-4-5i}=\frac{(-2+i)(-4+5i)}{16+25}=\frac{8-10i-4i-5}{16+25}=\frac{3-14i}{41}[/tex]
Therefore, the answer is:
[tex]\frac{-2+i}{-4-5i}=\frac{3}{41}-\frac{14}{41}i[/tex]
