wendy67 SImplify: Help Please! one year ago one year ago

1. Godfrey_Idrobo_Libreros

???

2. wendy67

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

3. No-data

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

4. No-data

$\sqrt{2}-i$

5. No-data

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

6. wendy67

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

7. No-data

Great!

8. No-data

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

9. wendy67

yes

10. wendy67

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

11. No-data

yes, now just make arithmetic operations.

12. wendy67

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

13. No-data

is there a specific anwer you need to get?

14. wendy67

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

15. No-data

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

16. wendy67

ok so how did you get that?