Question 998754: Find : z=(1-i)^23
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find : z=(1-i)^23
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Use DeMoivre
Note: 1-i is in QIV
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r = sqrt(1^2+1^2) = sqrt(2)
theta = arctan(-1/1) = arctan(-1) = 315 degrees or (7/4)pi
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(1-i)^23 = (sqrt(2))^23*cis(23(7/4)pi)
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= 2896.31*cis(40.25pi) = 2896.31*cis(pi/8)
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= 2896.31*cos(pi/8) + 2896.31*sin(pi/8)
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Cheers,
stan H.
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