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amarab
Group Title
simplify the expression?
would like help, not an answer.
6+i/5+i
 one year ago
 one year ago
amarab Group Title
simplify the expression? would like help, not an answer. 6+i/5+i
 one year ago
 one year ago

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etemplin Group TitleBest ResponseYou've already chosen the best response.0
http://www.sparknotes.com/math/algebra2/complexnumbers/section3.rhtml
 one year ago

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

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

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

amarab Group TitleBest ResponseYou've already chosen the best response.0
okay thanks! just what i needed
 one year ago

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

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
ok  glad you got it! :)
 one year ago

amarab Group TitleBest ResponseYou've already chosen the best response.0
okay 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??
 one year ago

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

asnaseer Group TitleBest 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
 one year ago
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