## amarab Group Title simplify the expression? would like help, not an answer. -6+i/-5+i one year ago one year ago

1. etemplin Group Title
2. asnaseer Group Title

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

3. amarab Group Title

a-bi?

4. asnaseer Group Title

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 Group Title

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

6. amarab Group Title

okay thanks! just what i needed

7. asnaseer Group Title

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

8. asnaseer Group Title

ok - glad you got it! :)

9. amarab Group Title

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 Group Title

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

11. irene22988 Group Title

i^2=-1

12. asnaseer Group Title

$\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