anonymous 4 years ago how do i simplify this?

1. anonymous

|dw:1327878261557:dw|

2. amistre64

conjugates i beleive

3. Mertsj

Numerator is 8i Denominator is 5-4i

4. Mertsj

Multiply numerator and denominator by 5+4i

5. amistre64

combine like terms under and the multiply it all by the conjugate of your denominator

6. amistre64

or stop anywhere along the way that your homework/text defines as simple enough

7. anonymous

i dont know how to do it, thats the problem

8. amistre64

which part, the multiply or the add?

9. amistre64

to combine like terms, just consider the "i" like any other variable

10. amistre64

7-6i -2 + 2i = 5 - 4i

11. anonymous

are you saying 5-4i is the answer?

12. amistre64

the conjugate thing might be overkill, since its hard to determine what is meant by "simplify"

13. amistre64

..... no, the denominator of a fraction is never "the answer" to an entire problem

14. amistre64

forgot the original problem :) $\frac{\sqrt{-64}}{5-4i}$

15. amistre64

the top simplifies to 8i since:$\sqrt{-64}=\sqrt{64*-1}=\sqrt{64}\sqrt{-1}=8i$

16. anonymous

these are my options

17. amistre64

then its a conjugate thing im sure :) $\frac{8i}{5-4i}*\frac{5+4i}{5+4i}=\frac{40i+32i^2}{25-16i^2}=\frac{40i-32}{25+16}$

18. amistre64

looks like it might shape up to the last one

19. anonymous

are you sure?

20. amistre64

well, from what ive written so far, im prettu sure -32 is -32; +40i is +40i; amd 25+16 is 41 ... so putting this altogether I tend to be leaning towards the last one since it fits all the parts :)

21. amistre64

typos not withstanding :)

22. anonymous

lol thank you !

23. amistre64

good luck, conjugates and is tend to not come up alot, so you have a tendency to forget about them

24. anonymous

yeah i've neverseen them until right now