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If 1 is a cube root of unity, then what is (1+ - ^2 )¹⁰⁰+ (1- + ^2 )¹⁰⁰ equal to?

Options

  1. A2¹⁰⁰ ^2
  2. B2¹⁰⁰
  3. C2¹⁰⁰
  4. D-2¹⁰⁰

Correct answer

D. -2¹⁰⁰

Step-by-step solution

aligned & Let I= (1+ - ^2 )¹⁰⁰+ (1- + ^2 )¹⁰⁰ & = (- ^2- ^2 )¹⁰⁰+(- - )¹⁰⁰ 1+ + ^2=0 & =2¹⁰⁰ ( ²⁰⁰+ ¹⁰⁰ ) & =2¹⁰⁰ ( ^2+ ) ^3=1 & =-2¹⁰⁰ . aligned

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