Question 1143530
solve:  (x+iy)^5 + (x-iy)^5 = -8
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C = x + iy ---> sqrt(2)cis(45)
D = x - iy ---> sqrt(2)cis(315)
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C^5 = sqrt(32)cis(225)
D^5 = sqrt(32)cis(1575) = sqrt(32)cis(135)
-8 = -8cis(0) = -8*1 + i*0
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C^5 = sqrt(32)*(-sqrt(2)/2 + i*(-sqrt(2)/2))
D^5 = sqrt(32)*(-sqrt(2)/2 + i*(sqrt(2)/2))
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C^5 + D^5 = -sqrt(64) = -8
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Did you mean solve?
Or confirm the identity?
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It's a confirmation of  the case that x & y are equal.  I forgot to state that.
If x <> y, then it's more tedious and not worth the effort without knowing what you want to do.