Question 617001: Calculate sqrt(3-3i). Give your answer in a+bi form. In polar form, use the angle 0<(theta)<2pi. Thank you!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Calculate sqrt(3-3i). Give your answer in a+bi form. In polar form, use the angle 0<(theta)<2pi.
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Polar form of 3-3i
r = sqrt(3^2 + 3^2) = 3sqrt(2)
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Note that (3,-3) is in the 4th Quadrant
theta = tan^-1(-1) = (7/4)pi
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General Form:
3 - 3i = sqrt(18)(cos[(7/4)pi+2npi) + isin((7/4)pi+2npi)]
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sqrt(3-3i) = ?
If n = 0 you get: 18^(1/4)(cos(7/8)pi + isin(7/8)pi) = (18^1/4 , (7/8)pi)
If n = 1 you get: 18^(1/4)(cos(15/8/pi + isin(15/8)pi)= (18^1/4 , (15/8)pi)
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Cheers,
Stan H.
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