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If is a complex cube root of unity, then 225+ (3 +8 ^2 )^2+ (3 ^2+8 )^2 is equal to:

Options

  1. A72
  2. B192
  3. C200
  4. D248

Correct answer

D. 248

Step-by-step solution

225+ (3 +8 ^2 )^2+ (3 ^2+8 )^2=225+9 ^2+64 ^4+48 ^3+9 ^4+64 ^2+48 ^3=225+9 ^2+64 +48+9 +64 ^2+48=225+73 ( ^2+ )+96=225-73+96=225+23=248

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