Question

-6+i/-5+i

Answer 1

\[\huge\ i=\sqrt{-1} \]

Answer 2

Although you wrote\[-6+\frac{ i }{ -5 }+i\]I assume you meant\[\frac{ -6+i }{ -5+i }\]
Use the sandard trick for dividing complex numbers:\[\frac{ a+bi }{ c+di }=\frac{ a+bi }{ c+di }\cdot \frac{ c-di }{ c-di }\]
Why? Because you don't want i in the denominator. Looking at the denominators, they give:\[(c+di)(c-di)=c^2-(di)^2=c^2-d^2i^2\]
Now that is where i²=-1 comes in!

So the new denominator is c² + d²

Try this with the numbers of your problem...