## anonymous one year ago TRIGONOMETRY: Write z = the square root of 3 minus i. in abbreviated trigonometric form.

1. anonymous

2. anonymous

fist find the magnitude?

3. anonymous

$Z=x+i y$ $|Z|=\sqrt{x^2+y^2}$

4. anonymous

So I just plug in y as -1 and x as root(3)? That's all there is to it?

5. anonymous

yes @dumbsearch2

6. anonymous

Then what?

7. anonymous

$\Theta=\tan^{-1}(\frac{ y }{ x }) =$$\Theta=\tan^{-1}(\frac{ -1 }{ \sqrt{3} })=-30^0$ in fourth quarter

8. anonymous

What is that?

9. anonymous

|dw:1441111202672:dw|

10. anonymous

I did: |Z| = root((root(3))^2+(-1)^2) and I found: |Z| = 2. What now?

11. anonymous

complex number: magnitude + angle

12. anonymous

How should I proceed? I found that |Z| = 2.

13. anonymous

this the magnitude, and now we should find the angle

14. anonymous

$\Theta=\tan^{-1}(\frac{ y }{ x }) =$$\tan^{-1}(\frac{ -1 }{ \sqrt{3} })=-30^0$

15. anonymous

$Z=x+iy=re^{i \theta}=r(\cos \theta+isin \theta)$=$rCis$ and$r=|Z|$

16. anonymous

r=|Z|=2

17. anonymous

$\theta=-30^0=330^0$

18. anonymous

Plug values of r & θ in: (rCis θ)

19. anonymous

Thank you so much! Most importantly, I know how to do the problem by myself now, in the clear manner in which you explained it... thanks a million!

20. anonymous

@dumbsearch2 no problem, you are welcome in any time.

21. anonymous

I want to do the same thing for the next problem: "Write z = -5 in abbreviated trigonometric form." However, why isn't there an i? Also how can I find the x and the y for the magnitude if there is only one variable (-5)?

22. anonymous

I finished complex course since 1 year only. it is interesting.

23. anonymous

Z=-5+i0

24. anonymous

x=-5, y=0

25. anonymous

Thank you!

26. anonymous

|Z| = 5, right?

27. anonymous

|dw:1441112765839:dw| not 0

28. anonymous

5 cis 180 degrees is the solution

29. anonymous

because a straight line is 180 degrees

30. anonymous

right?

31. anonymous

not, the angle is counted from positive x-axis

32. anonymous

A. 5 cis 180 degrees B. -5 cis 0 degrees C. root(5) cis 180 degrees D. 25 cis 0 degrees

33. anonymous

Which one?

34. anonymous

A

35. anonymous

thank you, I understand now.

36. anonymous

Good luck