Question

working on imaginary numbers
-2-3i/-3-4i
so when i did this i multiplied the top and bottom by the conjugate (3+4i) ...for the top i distributed and ended up with -6-9i-8i-12i^2 which ended up being 6-17i and for the bottom i got 7-24i i feel like my answer is very wrong but i'm not sure what i'm doing wrong? any help pleease?

Answer 1

The complex conjugate of -3-4i is -3+4i

So you have to multiply top and bottom by -3+4i

Answer 2

The whole point of multiplying a complex number by its conjugate is to turn a complex number into a real number

So the denominator should turn into a real number

Answer 3

oh. i seee. I just assumed I needed to make the negative in front go away too. Thank you! No wonder I was having a hard time.

Answer 4

you're welcome

tell me what you get

Answer 5

ughh. okay i did it, and i am not getting the right answer. for the top I ended up with
6+9i -8i -12i^2 and for the bottom i ended up with 9+12i-12i-16i^2 when i did everything in between I ended up with 18+i/25

Answer 6

that's correct, it's (18+i)/25 and that can be broken up into 18/25 + (1/25)*i

Answer 7

keep in mind that 18 + i/25 is not the same as (18+i)/25 because the first one looks like this \[\Large 18 + \frac{i}{25}\]

while the second one looks like this \[\Large\frac{18 + i}{25}\]

Answer 8

mine looked like 18+i/25

Answer 9

so the top and bottom will yield two different answers?

Answer 10

The answer is \[\Large \frac{18+i}{25}\] which breaks up into \[\Large \frac{18}{25}+\frac{1}{25}i\]

Answer 11

I'm not sure what you mean

Answer 12

I don't know what I mean either. thank you for breaking it down for me and helping me.

Answer 13

you're welcome