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amarab
 2 years ago
simplify the expression?
would like help, not an answer.
6+i/5+i
amarab
 2 years ago
simplify the expression? would like help, not an answer. 6+i/5+i

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etemplin
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.sparknotes.com/math/algebra2/complexnumbers/section3.rhtml

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2do you know what the conjugate of a complex number \((a+ib)\) is?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2correct. now notice what happens if you multiple a complex number by its conjugate:\[(a+bi)(abi)=a^2(bi)^2=a^2+b^2\]

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2i.e. the imaginary parts of a complex number disappear when you multiply it by its conjugate

amarab
 2 years ago
Best ResponseYou've already chosen the best response.0okay thanks! just what i needed

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2so the idea here is to multiply your fraction with something that would result in the denominator losing its imaginary part.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2ok  glad you got it! :)

amarab
 2 years ago
Best ResponseYou've already chosen the best response.0okay so i did... 6+i(5i) over 5+i(5i) then got 30+6i+5i+i^2 or 30+2i^2 but to the bottom... i ended up with 25+2i^2 and i don't know what to do after that??

amarab
 2 years ago
Best ResponseYou've already chosen the best response.0it looks like 30+2i^2/25+2i^2 but i know it's wrong

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2\[\frac{6+i}{5+i}=\frac{6+i}{5+i}\times\frac{5i}{5i}=\frac{(6+i)(5i)}{(5+i)(5i)}\]\[\qquad=\frac{30+6i5ii^2}{25+5i5ii^2}=\frac{30+ii^2}{25i^2}\]Then (as suggested by @irene22988) use the fact that \(i^2=1\) to simplify further
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