If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω2)100 + (1 - ω + ω2)100 equal to?  

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 2100 ω2
  2. 2100 ω 
  3. 2100
  4. -2100

Answer (Detailed Solution Below)

Option 4 : -2100
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Detailed Solution

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Explanation:

(1+ω +ω2)100(1-ω +ω2)100

= (– ω2 – ω2 )100 + (–ω – ω)100  {∵ 1 + ω  + ω2 = 0}

= 2100200 + ω100)

= 21002 + ω)     (∵ ω3 = 1)

= –2100 

∴ Option (d) is correct

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