Question 1030677: Find the roots of (-1+sqrt 3i)^3/2 leaving the answer in polar from.
Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the roots of (-1+sqrt 3i)^3/2 leaving the answer in polar from.
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Polar form:: r(cos(t)+i*sin(t))
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r = sqrt[1^2 + (sqrt(3))^2] = sqrt[4] = 2
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t = arctan(sqrt(3)/(-1)] = arctan(-sqrt(3)) = (2/3)pi
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Ans: r^(3/2)(cos[(2pi/3+2npi)/(3/2) + i*sin[(2pi/3+2npi)/(3/2)]
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If n = 0, Ans = r^(3/2)[cos[(4/9)pi + i*sin[(4/9)pi]
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If n = 1, Ans = r^(3/2)[cos[(4/9)pi+(4/3)pi] + isin[(4/9)pi + (4/3)pi]
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= r^(3/2)*cis[(16/9)pi]
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Cheers,
Stan H.
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