gfields444
How would i rationalize 6/ 3+i



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Outkast3r09
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multiply by the conjugate

Outkast3r09
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multiply by 1 using the conjugate*

estudier
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* top n bottom by 3i

gfields444
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So 9i?

estudier
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6(3i) / (3+i)(3i)

gfields444
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Is that all that I have to do? I'm not really sure how to do these sorts of problems

estudier
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You need to multiply out the brackets and simplify if possible

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

gfields444
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6(3i)? Wouldn't the bottom cancel itself out?

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

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

gfields444
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So confused

estudier
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Multiply it out and you will see...

gfields444
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9i/9

gfields444
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which you could divide 9 by 9 to get one, so i?

estudier
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6(3i) is 186i
Where do you get 9i from?

gfields444
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Oh wow opps. haha I added.

estudier
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Ok, now what do you get for the bottom?

gfields444
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9?

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

gfields444
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You multiply and the +i and i cancel out? i'm really sorry, this is new to me haha

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

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

gfields444
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estudier
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Right, so what is the bottom ( hintit is not 9)

gfields444
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8?

estudier
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9(1)

gfields444
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10

estudier
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Ok so finally you have 186i/10 which you can divide by 2 to get
93i/5 as a final answer.

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

gfields444
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thank you so much!!!

estudier
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ur welcome