SOLUTION: (3sqrt(3))/2 + (3)/(2)i Use De Moivre's Theorem to find the square of this complex number. Express the result in standard form. Thanks in advance.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: (3sqrt(3))/2 + (3)/(2)i Use De Moivre's Theorem to find the square of this complex number. Express the result in standard form. Thanks in advance.      Log On


   

Question 227691: (3sqrt(3))/2 + (3)/(2)i
Use De Moivre's Theorem to find the square of this complex number. Express the result in standard form.

Thanks in advance.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(3sqrt(3))/2 + (3)/(2)i
Use De Moivre's Theorem to find the square of this complex number. Express the result in standard form.
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r = sqrt[(3sqrt(3)/2)^2 + (3/2)^2) = sqrt(27/4 + 9/4) = 6/2 = 3
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theta = arctan[3sqrt(3)/2 / (3/2)] = arctan(sqrt(3)) = 60 degrees
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(3sqrt(3))/2 + (3)/(2)i = 3cis(60)
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Squaring you get: [3cis(60)]^2 = 9cis(120)
Then 9cis(120) = 9[cos(120) + isin(120)]
= 9[-1/2 + i(sqrt(3)/2)]
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= (-9/2) + i(9/2)sqrt(3)
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Cheers,
Stan H.