Respuesta :

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]

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