## anonymous 3 years ago Write the complex number in the form a + bi sqrt6(cos 315° + i sin 315°) PLEASE HELP

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1. anonymous

options are:

2. anonymous

@jim_thompson5910 could you help with this last one :/ ? Im so sorry

3. jim_thompson5910

what is the cosine of 315 degrees

4. anonymous

sqrt2/2

5. anonymous

@jim_thompson5910

6. jim_thompson5910

what about the sine of 315 degrees

7. anonymous

-1/sqrt2 @jim_thompson5910

8. jim_thompson5910

or -sqrt(2)/2

9. anonymous

sorry about that youre right ./.... typo @jim_thompson5910

10. jim_thompson5910

so this means that we have this so far $\Large \sqrt{6}\left(\cos(315) + i\sin(315)\right)$ $\Large \sqrt{6}\left(\frac{\sqrt{2}}{2} - i*\frac{\sqrt{2}}{2}\right)$

11. anonymous

so like (2-2i) sqrt3 @jim_thompson5910

12. jim_thompson5910

how did you get that

13. anonymous

I have no clue ... I messed up on the way Im thinking it was either A or C but Im leaning towards A

14. anonymous

@jim_thompson5910

15. jim_thompson5910

one sec

16. anonymous

okay

17. jim_thompson5910

$\Large \sqrt{6}\left(\cos(315) + i\sin(315)\right)$ $\Large \sqrt{6}\left(\frac{\sqrt{2}}{2} - i*\frac{\sqrt{2}}{2}\right)$ $\Large \sqrt{6}*\left(\frac{\sqrt{2}}{2}\right) - i*\sqrt{6}*\left(\frac{\sqrt{2}}{2}\right)$ $\Large \frac{\sqrt{6}*\sqrt{2}}{2} - i*\frac{\sqrt{6}*\sqrt{2}}{2}$ $\Large \frac{\sqrt{6*2}}{2} - i*\frac{\sqrt{6*2}}{2}$ $\Large \frac{\sqrt{12}}{2} - i*\frac{\sqrt{12}}{2}$ $\Large \frac{\sqrt{4*3}}{2} - i*\frac{\sqrt{4*3}}{2}$ $\Large \frac{\sqrt{4}*\sqrt{3}}{2} - i*\frac{\sqrt{4}*\sqrt{3}}{2}$ $\Large \frac{2*\sqrt{3}}{2} - i*\frac{2*\sqrt{3}}{2}$ $\Large \sqrt{3} - i*\sqrt{3}$ $\Large \sqrt{3} - \sqrt{3}*i$

18. anonymous

Thank you !!!

19. jim_thompson5910

np