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    Proving an identity in mathematics

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    Show that if z0 is an nth root of unity(z0 is not equal to 1) then
    1+z0+z0^2+...+z0^(n-1)=0.
    Hence show that
    cos(2Pi/1998)+cos(4Pi/1998)+...+cos(2Pi*1997/1998)=-1

    © BrainMass Inc. brainmass.com March 4, 2021, 5:39 pm ad1c9bdddf
    https://brainmass.com/math/complex-analysis/proving-identity-mathematics-5005

    Solution Preview

    Proof: Since z0 is an nth root of unity, z0^n=1.

    So
    (z0-1)(z0^(n-1)+z0^(n-2)+...+1)=0.

    Since z0 ...

    Solution Summary

    The solution contains a detailed proof of an equality involving the n-th root of unity.

    $2.49

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