## anonymous one year ago 2-5i/3i

1. anonymous

$\frac{ 2-5i }{ 3i }$

2. anonymous

I understand you are supposed to multiply by the conjugate, but what is the conjugate of 3i

3. anonymous

@Hero @nincompoop

4. zepdrix

The conjugate of $$\large\rm 0+3i$$ is $$\large\rm 0-3i$$

5. zepdrix

So therefore the conjugate of $$\large\rm 3i$$ is simply $$\large\rm -3i$$ k? :)

6. anonymous

don't be a slave to method you can multiply by $$i$$ top and bottom if you like or $$-i$$

7. zepdrix

Ya that'll save you a couple steps :D Seems like a good idea

8. anonymous

either way the denominator will become a real number, either 3 or -3 depending on which you pick

9. anonymous

I see thank you so much

10. anonymous

Wait, I get a different answer from when i multiply -3i to when i multiply from just i

11. anonymous

not after you cancel the common factor of 3

12. anonymous

which is why multiplying by $$-3i$$ is silly in this case

13. anonymous

ohhh so should the final answer be -2i -5

14. anonymous

idk i didn't do it want me to check?

15. anonymous

16. anonymous

no actually that can't be it

17. anonymous

$\frac{ 2-5i }{ 3i }\times \frac{i}{i}$ $=\frac{2i+5}{-3}$

18. anonymous

i got -6i -15 but then factored out 3

19. anonymous

yes but my answer has to be in complex number form i'm sorry i forgot to mention that

20. anonymous

now i am confused @satellite73 @zepdrix

21. anonymous

you mean in the form $$a+bi$$?

22. anonymous

yes

23. anonymous

break it in to two pieces is all

24. anonymous

for example $\frac{7+8i}{5}=\frac{7}{5}+\frac{8}{5}i$

25. anonymous

oh i understand now can i get back to you in a minute with my answer?

26. anonymous

is this correct? $\frac{ 2i }{ -3 }+\frac{ 5 }{ -3 }$

27. beginnersmind

Yes, although you might want to write it as $-\frac{ 5 }{ 3 } -\frac{ 2 }{ 3 }i$ or even $\frac{ -5-2i }{ 3 }$ but it's just cosmetical at this point.

28. anonymous

thank you so much

29. beginnersmind

No problem, satellite did all the work though. ;)