## marigirl one year ago write z=1 - √3 i in polar form I got my r = 2 and i got arg (theta) value as -pi/3

1. marigirl

the answer reads: (g) The modulus of 1 - √3 i is √12 + (√3)2 = 2 and its argument θ satisfies tan θ = - √3/1 = - √3, whence θ is equal to either 2π/3 or 5π/3. Since y=-√3 is negative, we have θ = 5π/3. The polar form of -3 + 3i is thus 2 (cos 5π/3 + i sin 5π/3). ....

2. marigirl

|dw:1441322582245:dw| Thats what i thought

3. marigirl

this example too seems to be adding when i thought arg (theta) is positive $-\pi < \theta \le \pi$

4. marigirl

unless im just confused.

5. marigirl

@jdoe0001

6. anonymous

im still confused

7. anonymous

that has to be the ugliest circle i have ever seen

8. anonymous

9. marigirl

Umm no that's not a circle

10. marigirl

I was trying to show that when the Arg theta value is between 0 and 180deg then it's positive

11. freckles

12. freckles

|dw:1441326527937:dw|

13. marigirl

Yes so should it be a negative and I got negative pi/3

14. freckles

|dw:1441326541656:dw|

15. freckles

right -pi/3 is right

16. freckles

but

17. marigirl

18. freckles

it looks like they wanted you to write theta in between 0 and 2pi based on their answer

19. freckles

so you just do -pi/3+2pi

20. freckles

this will put you between 0 and 2pi

21. freckles

i see you wanted to add pi for some reason but that would put you in the second quadrant

22. freckles

|dw:1441326754891:dw| doing theta+pi will put you in second quadrant as you can see

23. freckles

and we definitely want to be in 4th

24. freckles

theta+2pi would get us back there to fourth quadrant

25. marigirl

If the question doesn't specify will -pi/3 also be a sufficient answer

26. freckles

yes if they don't specify what they want theta between yes -pi/3 will do and so would -pi/3+2pi*n where n is an integer as long as you keep your r positive that is

27. marigirl

Also can u look at the image I have attached above...I guess they have demonstrated both methods

28. freckles

$(r,\theta)=(r,\theta+2 \pi n) \\ \text{ or } \\ (r,\theta)=(-r,\theta+\pi+2 \pi n)$

29. freckles

when it comes to polar coordinates there is not a unique way to express one point

30. freckles

not a unique way meaning there are infinite amount of ways to express one point

31. freckles

so you could haven chosen (-2,2pi/3)

32. anonymous

on account of sine and cosine are periodic functions with period $$2\pi$$

33. freckles

or (2,5pi/3) or (2,-pi/3)

34. freckles

and so on