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AP EAMCET2010MathematicsComplex Number

If is a complex cube root of unity, then (x+1)(x+ )(x- -1) is equal to

Options

  1. Ax^3-1
  2. Bx^3+1
  3. Cx^3+2
  4. Dx^3-2

Correct answer

A. x^3-1

Step-by-step solution

cube root of unity ie, ^3=1 and 1+ + ^2=0 Then, (x+1)(x+ )(x- -1)=(x+1) (x^2+ x- x- ^2-x- )=(x+1) (x^2-x- ( + ^2 ) )=(x+1) (x^2-x-(-1) ) ( + ^2=-1 )=(x+1) (x^2-x+1 )=(x+1) (x^2+1-x )= (x^3-1 )

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