anonymous one year ago Write the complex number in the form a + bi. square root of six(cos 315° + i sin 315°)

1. anonymous

I dont know how to solve this at all... My choices: square root of three over two minus square root of thee over two times i square root of six minus square root of sixi square root of three minus square root of threei square root of six over two minus square root of six over two times i

2. Nnesha

look at the unit circle cos 315 = what ? remember (x,y) sin =y-coordinate and cos = x-coordinate

3. anonymous

cos315 is square root(2)/2

4. anonymous

so $\frac{ \sqrt{2} }{ 2 }$ is my x coordinate?

5. Nnesha

|dw:1439174169775:dw|

6. anonymous

Yes, I was just looking at that

7. Nnesha

$\huge\rm \sqrt{6}(\cos 315° + i \sin 315°)$ so cos 315 =sqrt{2} over 2 replace cos 315 by that

8. anonymous

So i would replace isin315 with $\frac{ -\sqrt{2} }{ 2 }$

9. Loser66

@Nnesha Good job!! open my eye!! :)

10. Nnesha

$\huge\rm \sqrt{6}(\color{reD}{cos 315°} + i \sin 315°)$ $\sqrt{6}(\frac{ \sqrt{2} }{ 2 }+i (-\frac{ \sqrt{2} }{ 2 }))$ ust sin315 not the i

11. Nnesha

just**

12. anonymous

Alright, then do I distribute the $\sqrt{6}$?

13. Nnesha

thanks o^_^o @66

14. Nnesha

first distribute by i i times -sqrt{2} over 2

15. Nnesha

$\sqrt{6}(\frac{ \sqrt{2} }{ 2} - \frac{ \sqrt{2} }{ 2}i)$

16. anonymous

Okay, after distributing i, do I distribute the square root of 6?

17. Nnesha

well i wouldn't do that just take out the common factor

18. Nnesha

$\sqrt{6}\color{ReD}{(\frac{ \sqrt{2} }{ 2} - \frac{ \sqrt{2} }{ 2}i)}$ what is common factor in the parentheses

19. anonymous

Hmm... then my end result is $\sqrt{3}(-i+1)$

20. Nnesha

u sure or just guessing ? ;P

21. anonymous

100% sure. I just calculated it. If I distribute the square root of 3, then I get what appears to be my third choice. Am I correct?

22. Nnesha

alright yes that's correct there are square roots that's why i don't like distributing by sqrt{6} you can take out the common factor which is sqrt{2}/2

23. anonymous

Oh, I see. @Nnesha

24. Nnesha

$\sqrt{6} \times \frac{ \sqrt{2} }{ 2 }(1-i)$ $\frac{ \sqrt{12} }{ 2 }(1-i)$multply sqrt{6} times sqrt{2} now factor 12 $\frac{ \sqrt{4 \times 3} }{ 2}(1-i)$ take the square root of 2 you will get the same answer

25. Nnesha

i found it easy but you can apply any method as lng s you get the same answer