simplify the expression?

would like help, not an answer.

-6+i/-5+i

Question

simplify the expression?

would like help, not an answer.

-6+i/-5+i

anonymous · Answer

http://www.sparknotes.com/math/algebra2/complexnumbers/section3.rhtml

asnaseer · Answer

do you know what the conjugate of a complex number $(a+ib)$ is?

amarab · Answer

a-bi?

asnaseer · Answer

correct.
now notice what happens if you multiple a complex number by its conjugate:$$(a+bi)(a-bi)=a^2-(bi)^2=a^2+b^2$$

asnaseer · Answer

i.e. the imaginary parts of a complex number disappear when you multiply it by its conjugate

amarab · Answer

okay thanks! just what i needed

asnaseer · Answer

so the idea here is to multiply your fraction with something that would result in the denominator losing its imaginary part.

asnaseer · Answer

ok - glad you got it! :)

amarab · Answer

okay so i did... -6+i(-5-i) over -5+i(-5-i)
then got 30+6i+-5i+-i^2 or 30+2i^2
but to the bottom... i ended up with 25+2i^2
and i don't know what to do after that??

amarab · Answer

it looks like 30+2i^2/25+2i^2
but i know it's wrong

anonymous · Answer

i^2=-1

asnaseer · Answer

$$\frac{-6+i}{-5+i}=\frac{-6+i}{-5+i}\times\frac{-5-i}{-5-i}=\frac{(-6+i)(-5-i)}{(-5+i)(-5-i)}$$$$\qquad=\frac{30+6i-5i-i^2}{25+5i-5i-i^2}=\frac{30+i-i^2}{25-i^2}$$Then (as suggested by @irene22988) use the fact that $i^2=-1$ to simplify further