wendy67
SImplify:
Help Please!



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wendy67
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\[\frac{ 1+2i }{ \sqrt{2}+i }\]

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Multiply both numerator and denominator by the conjugate of the denominator.I mean

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\[\sqrt{2}i\]

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\[\frac{1+2i}{\sqrt{2}+i}\cdot \frac{\sqrt{2}i}{\sqrt{2}i}\]

wendy67
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I got:
\[\frac{ \sqrt{2}i+2i \sqrt{2}2i ^{2} }{ 2i ^{2}}\]

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Great!

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but also you know that \[i^2=1\]

wendy67
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yes

wendy67
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so, it would be:
\[\frac{ \sqrt{2}i+2i \sqrt{2}2(1) }{ 2(1) }\]

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yes, now just make arithmetic operations.

wendy67
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ok i got:
\[\frac{ \sqrt{2}i+2i \sqrt{2}+2 }{ 3 }\]
and this where i got stuck

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is there a specific anwer you need to get?

wendy67
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yes i should get :
\[\frac{ 2+\sqrt{2} }{ 3 }+\frac{ 2\sqrt{2}1 }{ 3 }\]

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I got: \[\frac{\sqrt{2}+2}{3}\frac{1+2\sqrt{2}}{3}i\]

wendy67
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ok so how did you get that?