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COMEDK2012MathematicsComplex Number

If 1, , ² are the cube roots of unity, then (3+3 ²+5 )⁶- (2+6 ²+2 )³ is equal to

Options

  1. A32
  2. B64
  3. C0
  4. D-1

Correct answer

C. 0

Step-by-step solution

We have, aligned (3& .+3 ²+5 )⁶- (2+6 ²+2 )³ &= [3 (1+ ² )+5 ]⁶- [2(1+ )+6 ² ]³ &=[3(- )+5 ]⁶- [2 (- ² )+6 ² ]³ &=(2 )⁶- (4 ² )³ &=2⁶ ⁶-64 ⁶ &=64-64=0 aligned

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