Question

How would i rationalize 6/ 3+i

Answer 1

multiply by the conjugate

Answer 2

multiply by 1 using the conjugate*

Answer 3

* top n bottom by 3-i

Answer 4

So 9i?

Answer 5

6(3-i) / (3+i)(3-i)

Answer 6

Is that all that I have to do? I'm not really sure how to do these sorts of problems

Answer 7

You need to multiply out the brackets and simplify if possible

Answer 8

Just like normal except you have i's to deal with...

Answer 9

6(3-i)? Wouldn't the bottom cancel itself out?

Answer 10

It is a kind of trick to get rid of the i on the bottom.....

Answer 11

Similar to how you get rid of a rdical, same sort of idea...

Answer 12

So confused

Answer 13

Multiply it out and you will see...

Answer 14

9-i/9

Answer 15

which you could divide 9 by 9 to get one, so -i?

Answer 16

6(3-i) is 18-6i
Where do you get 9-i from?

Answer 17

Oh wow opps. haha I added.

Answer 18

Ok, now what do you get for the bottom?

Answer 19

9?

Answer 20

You have (3+i)(3-i)
Tell me how it comes to 9

Answer 21

You multiply and the +i and -i cancel out? i'm really sorry, this is new to me haha

Answer 22

(3+i)(3-i) is 3*3 + 3*i -3*i - i^2 (using FOIL?)

Answer 23

So the 3i's cancel out and leave 9-i^2
So what is i^2 ?

Answer 24

-1

Answer 25

Right, so what is the bottom ( hint-it is not 9)

Answer 26

8?

Answer 27

9-(-1)

Answer 28

10

Answer 29

Ok so finally you have 18-6i/10 which you can divide by 2 to get
9-3i/5 as a final answer.

Answer 30

So, procedure for these is *by conjugate top and bottom then simplify

Answer 31

thank you so much!!!

Answer 32

ur welcome