SOLUTION: please help with the following question i just cant figure it out it says Find the three cube roots of Z = 5cos225degrees + jsin 225degrees and show these on an argand diagram Wh

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Question 445902: please help with the following question i just cant figure it out it says
Find the three cube roots of Z = 5cos225degrees + jsin 225degrees and show these on an argand diagram
Which of these roots is the PRINCIPAL ROOT?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find the three cube roots of Z = 5cos225degrees + jsin 225degrees and show these on an argand diagram
Which of these roots is the PRINCIPAL ROOT?
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Z^(1/3) = 5^(1/3)[cos(225+360n)/3 + jsin(225+360n)]
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Let n = 0 then z^(1/3) = 5^(1/3)[cos(75) + jsin(75)]
That is the principal root
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Let n = 1 then z^(1/3) = 5^(1/3)[cos(195) + jsin(195)]
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Let n = 2 then z^(1/3) = 5^(1/3)[cos(315) + jsin(315)]
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Those are the 3 cube roots.
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Cheers,
Stan H.