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anonymous
 one year ago
Which expression is a CUBE ROOT of 2i?
A. cubert(2) (cos(260 degree) + i sin(260 degree))
B. cubert(2) (cos(60 degree) + i sin(60 degree))
C. cubert(2) (cos(90 degree) + i sin(90 degree))
D. cubert(2) (cos(210 degree) + i sin(210 degree))
anonymous
 one year ago
Which expression is a CUBE ROOT of 2i? A. cubert(2) (cos(260 degree) + i sin(260 degree)) B. cubert(2) (cos(60 degree) + i sin(60 degree)) C. cubert(2) (cos(90 degree) + i sin(90 degree)) D. cubert(2) (cos(210 degree) + i sin(210 degree))

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would it be D? (Using improper math)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To approach this problem, you should write the complex number in polar form.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok! So it would be r = 2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For simplicity, let's pull out the 2 for now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Use Euler's identity to write i.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Remember i is 90 degrees on the complex plane.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So\[i = e^{ i \pi/2} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now to find the cube root of just i, you can divide the exponent of the polar form by 3.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt[3]{i} = e^{i \pi/6}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now rewrite the polar form into rectangular form.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And multiply with the cube root of 2, a negative real constant.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt[3]{2}= e ^{ipi/6}\]Sorry, I don't know how to do this area

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Write it like this: \[e^{i \pi/6} = \cos(\pi/6) + i \sin(\pi/6)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now in your question, it seems that they are representing the answers in degrees and also they are incorporating the negative factor into the complex part.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You will need to rewrite the angles in degree form, and also rotate by 90 degrees.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So \[\frac{ \pi }{ 6} = 30\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And then it would be in the 3rd quadent?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh sorry, I meant rotate by 180 degrees.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok! So that makes it 210 degrees, which is answer D!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great! Thank you for your help and taking the time to explain this to me!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's my pleasure. Good luck.
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