Question 423089: find all seventh roots of 3+4i please try and give all steps...
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find all seventh roots of 3+4i please try and give all steps...
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r = sqrt(3^2+4^2) = 5
theta = tan^-1(4/3) = 53.13 degrees
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(3+4i)^(1/7) = 5^(1/7)(cis(53.13+360n)/7)
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To find the 7 roots let n = 0,1,2,3,...,6
Note: 360/7 = 51.43 degrees
and 53.13/7 = 7.59
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So for n = 3 you get: 5^(1/7)cis(7.59+3(41.43))
etc.
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Cheers,
Stan H.
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