marigirl
  • marigirl
write z=1 - √3 i in polar form I got my r = 2 and i got arg (theta) value as -pi/3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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marigirl
  • 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
  • marigirl
|dw:1441322582245:dw| Thats what i thought
marigirl
  • marigirl
this example too seems to be adding when i thought arg (theta) is positive \[-\pi < \theta \le \pi \]
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marigirl
  • marigirl
unless im just confused.
marigirl
  • marigirl
@jdoe0001
anonymous
  • anonymous
im still confused
anonymous
  • anonymous
that has to be the ugliest circle i have ever seen
anonymous
  • anonymous
correct answer though
marigirl
  • marigirl
Umm no that's not a circle
marigirl
  • marigirl
I was trying to show that when the Arg theta value is between 0 and 180deg then it's positive
freckles
  • freckles
|dw:1441326450077:dw| your point is in the 4th quadrant
freckles
  • freckles
|dw:1441326527937:dw|
marigirl
  • marigirl
Yes so should it be a negative and I got negative pi/3
freckles
  • freckles
|dw:1441326541656:dw|
freckles
  • freckles
right -pi/3 is right
freckles
  • freckles
but
marigirl
  • marigirl
Why haa the model answera added 3pi/2 to pi/3
freckles
  • freckles
it looks like they wanted you to write theta in between 0 and 2pi based on their answer
freckles
  • freckles
so you just do -pi/3+2pi
freckles
  • freckles
this will put you between 0 and 2pi
freckles
  • freckles
i see you wanted to add pi for some reason but that would put you in the second quadrant
freckles
  • freckles
|dw:1441326754891:dw| doing theta+pi will put you in second quadrant as you can see
freckles
  • freckles
and we definitely want to be in 4th
freckles
  • freckles
theta+2pi would get us back there to fourth quadrant
marigirl
  • marigirl
If the question doesn't specify will -pi/3 also be a sufficient answer
freckles
  • 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
  • marigirl
Also can u look at the image I have attached above...I guess they have demonstrated both methods
freckles
  • freckles
\[(r,\theta)=(r,\theta+2 \pi n) \\ \text{ or } \\ (r,\theta)=(-r,\theta+\pi+2 \pi n)\]
freckles
  • freckles
when it comes to polar coordinates there is not a unique way to express one point
freckles
  • freckles
not a unique way meaning there are infinite amount of ways to express one point
freckles
  • freckles
so you could haven chosen (-2,2pi/3)
anonymous
  • anonymous
on account of sine and cosine are periodic functions with period \(2\pi\)
freckles
  • freckles
or (2,5pi/3) or (2,-pi/3)
freckles
  • freckles
and so on

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