यदि 1, ω, ω2  एकल के घन मूल हैं, तो (1 + ω) (1 + ω2) (1 + ω4) (1 + ω8) का मान क्या है?

  1. -1
  2. 0
  3. 1
  4. 2
  5. इनमें से कोई नहीं

Answer (Detailed Solution Below)

Option 3 : 1
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संकल्पना:

यदि 1, ω, ω2 एकल के घन मूल हैं। 

  • 1 + ω + ω2 = 0
  • ω3 = 1

 

गणना:

हमें (1 + ω) (1 + ω2) (1 + ω4) (1 + ω8) का मान ज्ञात करना है

⇒ (1 + ω) (1 + ω2) (1 + ω4) (1 + ω8)

= [(1 + ω) (1 + ω2)] × [(1 + ω3 × ω) (1 + (ω3)2 ω2)]

= [(1 + ω) (1 + ω2)] × [(1 + ω) (1 + ω2)]      (∵ω3 = 1)

= (1 + ω + ω2 + ω3) × (1 + ω + ω2 + ω3)

= (0 + 1) × (0 + 1)

= 1 × 1 = 1

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