anonymous
  • anonymous
SImplify: Help Please!
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
???
anonymous
  • anonymous
\[\frac{ 1+2i }{ \sqrt{2}+i }\]
anonymous
  • anonymous
Multiply both numerator and denominator by the conjugate of the denominator.I mean

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anonymous
  • anonymous
\[\sqrt{2}-i\]
anonymous
  • anonymous
\[\frac{1+2i}{\sqrt{2}+i}\cdot \frac{\sqrt{2}-i}{\sqrt{2}-i}\]
anonymous
  • anonymous
I got: \[\frac{ \sqrt{2}-i+2i \sqrt{2}-2i ^{2} }{ 2-i ^{2}}\]
anonymous
  • anonymous
Great!
anonymous
  • anonymous
but also you know that \[i^2=-1\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
so, it would be: \[\frac{ \sqrt{2}-i+2i \sqrt{2}-2(-1) }{ 2-(-1) }\]
anonymous
  • anonymous
yes, now just make arithmetic operations.
anonymous
  • anonymous
ok i got: \[\frac{ \sqrt{2}-i+2i \sqrt{2}+2 }{ 3 }\] and this where i got stuck
anonymous
  • anonymous
is there a specific anwer you need to get?
anonymous
  • anonymous
yes i should get : \[\frac{ 2+\sqrt{2} }{ 3 }+\frac{ 2\sqrt{2}-1 }{ 3 }\]
anonymous
  • anonymous
I got: \[\frac{\sqrt{2}+2}{3}-\frac{1+2\sqrt{2}}{3}i\]
anonymous
  • anonymous
ok so how did you get that?

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