Respuesta :

To put

[tex]\frac{5}{7-i}[/tex]

In the standard form, we must multiply the numerator and denominator by the complex conjugate of (7-i), it means

[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}[/tex]

And now we solve it, therefore

[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}=\frac{5(7+i)}{7^2-i^2}[/tex]

Remember that

[tex]i^2=-1[/tex]

Then

[tex]\begin{gathered} \frac{5(7+i)}{7^2-i^2}=\frac{5(7+i)}{49+1} \\ \\ \frac{5(7+i)}{49+1}=\frac{5(7+i)}{50} \end{gathered}[/tex]

Now we can simplify it

[tex]\frac{5(7+i)}{50}=\frac{7+i}{10}[/tex]

And we have it in the standard form

[tex]\frac{7}{10}+\frac{1}{10}i[/tex]