anonymous
  • anonymous
True or False: When its argument is restricted to [0, 2pi), the polar form of a complex number is not unique.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I think it's false
freckles
  • freckles
|dw:1438653320969:dw| let's think about rewriting this polar coordinate so that theta is between 0 and 360
freckles
  • freckles
|dw:1438653367482:dw|

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freckles
  • freckles
but what happens when you change the sign of that other r
freckles
  • freckles
for example where is (-3,225 deg)
anonymous
  • anonymous
\[(3\sqrt{2}/2, 3\sqrt{2}/2)\] ?
anonymous
  • anonymous
wait it would be -3root2/2, -3root2/2 right?
freckles
  • freckles
|dw:1438653913563:dw| I was going for that if you change the sign of the r it goes in the opposite direction on that same line there
anonymous
  • anonymous
Oh okay yes
freckles
  • freckles
if you want to write both and Cartesian coordinates you can... \[(r=3,\theta=45 \deg) \\ x=r cos(\theta)= 3 \cos(45) =3 \frac{\sqrt{2}}{2} =\frac{ 3 \sqrt{2}}{2} \\ y =r \sin(\theta)= 3 \sin(45) =3 \frac{\sqrt{2}}{2}= \frac{3 \sqrt{2}}{2} \\ (r=-3, \theta=225 \deg) \\ x =rcos(\theta)=-3 \cos(225)=-3 \frac{-\sqrt{2}}{2}=\frac{3 \sqrt{2}}{2} \\ y=r \sin(\theta)= -3 \sin(225) -3 \frac{-\sqrt{2}}{2}=\frac{3 \sqrt{2}}{2}\]
freckles
  • freckles
as you they both converted to the same Cartesian coordinate pair
freckles
  • freckles
and both have their theta's between 0 and 360 deg
anonymous
  • anonymous
So they are not all unique
freckles
  • freckles
When its argument is restricted to [0,2pi), we can still find 2 polar points one with a negative r and one with a positive r. So not unique. If they had said: When its argument is restricted to [0,2pi) where r>0, then the polar coordinate is unique.
freckles
  • freckles
If they had said: When its argument is restricted to [0,2pi) where r>0, then the polar coordinate is unique. then this would be true <---forgot to add this last line
anonymous
  • anonymous
Okay so it would be true
anonymous
  • anonymous
Awesome! Thank you so much
freckles
  • freckles
right not unique unique means we can only find one but we found two
anonymous
  • anonymous
hmmm @freckles it was false. Should I ask my teacher if the question is wrong?
freckles
  • freckles
it is true since \[(r,\theta)=(-r, \theta+\pi) \text{ if } \theta \in [0,\pi) \\ (r,\theta)=(-r,\theta-\pi) \text{ if } \theta \in [\pi,2\pi]\]
freckles
  • freckles
yep in either case there is no one way to write the complex number with restriction that theta has to be between 0 and 2pi
anonymous
  • anonymous
Ya I understand the explanation. Should be right. So I'll just have to ask her next time I see her! Thank you for your help!
freckles
  • freckles
np
freckles
  • freckles
http://openstudy.com/study#/updates/53796108e4b0e5430795a83f this question is almost the same question
freckles
  • freckles
i wonder if maybe they were just changing things on the homework to make it not identical but maybe forgot to change some of the answers

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