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amarab
Group Title
simplify the expression?
would like help, not an answer.
6+i/5+i
 2 years ago
 2 years ago
amarab Group Title
simplify the expression? would like help, not an answer. 6+i/5+i
 2 years ago
 2 years 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
 2 years 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?
 2 years 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:\[(a+bi)(abi)=a^2(bi)^2=a^2+b^2\]
 2 years 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
 2 years ago

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

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