## amarab 3 years ago simplify the expression? would like help, not an answer. -6+i/-5+i

1. etemplin
2. asnaseer

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

3. amarab

a-bi?

4. asnaseer

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

5. asnaseer

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

6. amarab

okay thanks! just what i needed

7. asnaseer

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

8. asnaseer

ok - glad you got it! :)

9. amarab

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??

10. amarab

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

11. irene22988

i^2=-1

12. asnaseer

$\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