AP EAMCET202316 May 2023Morning ShiftMathematicsComplex NumberActual

If is a complex cube root of unity, then ( _ k=1 ^7(k- ) (k- ^2 ) 175 )=

Options

Correct answer

A. -1

Step-by-step solution

We have to calculate ( _ k=1 ^7(k- ) (k- ^2 ) 175 )= ( _ k=1 ^7 (k^2-k ^2-k + ^3 ) 175 )= ( _ k=1 ^7 (k^2-k x(-1)+1 ) 175 )= ( 175 ( _ k=1 ^7 k^2+ _ k=1 ^7 k+ _ k=1 ^7 1 ) )= ( 175 ( 1 6 7 (7+1) (2 7+1)+ 1 2 7 8+7 ) )= ( 175 (140+28+7) )= ( 175 175 )= ( )=-1 .

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