Complex No.

If (z+1)^7+z^7=0 , then find \sum_{k=0}^{k=6} \text{Re}(z_k) , where z_k are roots of the the given equation.

1 Answers

=> (1 + 1/z)⁷ = -1
=> 1 + 1/z = e^ix ...where x = (2k+1)Ï€7
=> ....
=> ....
=> Re(z) = (cosx-1)2(1-cosx) = -12
=> answer to the Q = -72

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