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

- marigirl

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

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- 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).
....

- marigirl

|dw:1441322582245:dw|
Thats what i thought

- marigirl

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

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## More answers

- marigirl

unless im just confused.

- marigirl

@jdoe0001

- anonymous

im still confused

- anonymous

that has to be the ugliest circle i have ever seen

- anonymous

correct answer though

- marigirl

Umm no that's not a circle

- marigirl

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

- freckles

|dw:1441326450077:dw|
your point is in the 4th quadrant

- freckles

|dw:1441326527937:dw|

- marigirl

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

- freckles

|dw:1441326541656:dw|

- freckles

right -pi/3 is right

- freckles

but

- marigirl

Why haa the model answera added 3pi/2 to pi/3

- freckles

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

- freckles

so you just do -pi/3+2pi

- freckles

this will put you between 0 and 2pi

- freckles

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

- freckles

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

- freckles

and we definitely want to be in 4th

- freckles

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

- marigirl

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

- 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

- marigirl

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

- freckles

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

- freckles

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

- freckles

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

- freckles

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

- anonymous

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

- freckles

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

- freckles

and so on

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