Question

simplify the expression
-6+i/-5+i

Answer 1

"simplify" the expression when it's a complex rational, just means, get rid of the peski "i" in the denominator, you'd do that using the conjugate of the denominator, and multiply top and bottom by it, that is \(\bf \cfrac{-6+i}{-5+i}\times \cfrac{-5-i}{-5-i}\implies \cfrac{(-6+i)(-5-i)}{(-5+i)(-5-i)}\\ \quad \\
\textit{keep in mind that}\qquad (a-b)(a+b) = a^2-b^2\qquad thus\\ \quad \\
\cfrac{(-6+i)(-5-i)}{(-5+i)(-5-i)}\implies \cfrac{(-6+i)(-5-i)}{(-5)^2-(i)^2}
\)

Answer 2

simplify that, to get the "simplified " equation