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anonymous
 one year ago
Which expression is a cube root of 1 + i sqrt(3)?
A. cubert(2) (cos(120degrees) + i sin(120 degrees))
B. cubert(2) (cos(40 degrees) + i sin(40 degrees))
C. cubert(2) (cos(280 degrees) + i sin(280 degrees))
D. cubert(2) (cos(320 degrees) + i sin(320 degrees))
***My Answer: D***
Please Help!!!
anonymous
 one year ago
Which expression is a cube root of 1 + i sqrt(3)? A. cubert(2) (cos(120degrees) + i sin(120 degrees)) B. cubert(2) (cos(40 degrees) + i sin(40 degrees)) C. cubert(2) (cos(280 degrees) + i sin(280 degrees)) D. cubert(2) (cos(320 degrees) + i sin(320 degrees)) ***My Answer: D*** Please Help!!!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[1+\sqrt{3}=r \left( \cos \theta+\iota \sin \theta \right)\] \[r \cos \theta =1,r \sin \theta =\sqrt{3}\] square and add and find r divide find theta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I would do r = 1cos(theta), r = 3sin^2(theta)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[r^2\cos ^2\theta =1,r^2\sin ^2\theta=3\] \[r^2\left( \cos ^2\theta+\sin ^2\theta \right)=1+3=4\] r=2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0r is always positive ,so \[\cos~ \theta~ is~ negative~and~\sin \theta~is~positive.\] so angle lies in second quadrant. now divide to find theta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would \[\theta = 120\] be the angle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no guess ,show me your calculations.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok \[r ^{2}(\cos ^{2}\theta + \sin ^{2}\theta)\]\[2 (\cos ^{2}\theta + \sin ^{2}\theta)\] \[1 + i \sqrt{3}\] \[\theta = \frac{ \sqrt{3} }{ 1}\]\[\theta = \frac{ \pi }{ 3}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That is all I know of. Not exactly sure if it is correct. Sorry

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ r \sin \theta }{ r \cos \theta }=\frac{ \sqrt{3} }{ 1 }=\sqrt{3}=\tan 60=\tan \left( 18060\right) =\tan 120\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\tan \theta=\tan 120,\theta=120\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh wow I was far off but at the same time I kinda sorta knew what I was doing. Haha. I answer would now be A I'm assuming. Thank you for taking the time to explain this to me. I desperately needed the help.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[1+i \sqrt{3}=2\left( \cos 120+i \sin 120 \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh wait the answer would be B

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh sorry you wanted cube root ,i have not noticed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's ok :) I already hit the submit button haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wouldn't you just divide 120/3 to get 40?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[1+i \sqrt{3}=2\left( \cos( 120+360n)+i \sin \left( (120+360n \right) \right)\] \[or Z ^{\frac{ 1 }{ 3 }}=2^1/3e ^{\frac{ 360n+120 }{ 3 }}\] put n=0,1,2 ,you get all the three cube roots

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\left( 1+i \sqrt{3} \right)^{\frac{ 1 }{ 3 }}=2^{\frac{ 1 }{ 3 }}\left\{ \cos \left( \frac{ 360n+120 }{ 3 }+i \sin \left( \frac{ 360n+120 }{ 3 } \right)\right)\right\}\] put n=0,1,2 you get all the values.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much! I very much appreciate it!
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