## anonymous 3 years ago SImplify: Help Please!

1. anonymous

???

2. anonymous

$\frac{ 1+2i }{ \sqrt{2}+i }$

3. anonymous

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

4. anonymous

$\sqrt{2}-i$

5. anonymous

$\frac{1+2i}{\sqrt{2}+i}\cdot \frac{\sqrt{2}-i}{\sqrt{2}-i}$

6. anonymous

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

7. anonymous

Great!

8. anonymous

but also you know that $i^2=-1$

9. anonymous

yes

10. anonymous

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

11. anonymous

yes, now just make arithmetic operations.

12. anonymous

ok i got: $\frac{ \sqrt{2}-i+2i \sqrt{2}+2 }{ 3 }$ and this where i got stuck

13. anonymous

is there a specific anwer you need to get?

14. anonymous

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

15. anonymous

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

16. anonymous

ok so how did you get that?