Question

SImplify:
Help Please!

Answer 1

???

Answer 2

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

Answer 3

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

Answer 4

\[\sqrt{2}-i\]

Answer 5

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

Answer 6

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

Answer 7

Great!

Answer 8

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

Answer 9

yes

Answer 10

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

Answer 11

yes, now just make arithmetic operations.

Answer 12

ok i got:
\[\frac{ \sqrt{2}-i+2i \sqrt{2}+2 }{ 3 }\]

and this where i got stuck

Answer 13

is there a specific anwer you need to get?

Answer 14

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

Answer 15

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

Answer 16

ok so how did you get that?