यदि 1, ω, ω2  एकल के घनमूल हैं तो मान इस प्रकार है

(1 + ω2)(1 + ω4)(1 + ω8)(1 + ω16) क्या है?

  1. -1
  2. 0
  3. 1
  4. 2
  5. -2

Answer (Detailed Solution Below)

Option 3 : 1
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Detailed Solution

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संकल्पना:

यदि 1, ω, ω2  एकल के घनमूल हैं

  • ω=1+i32 और ω2=1i32
  • ω3k=1, ω3k+1=ω, ω3k+2=ω2 ---- (1)
  • 1 + ω + ω2 = 0 और ω3 = 1      ----(2)

गणना:

हमारे पास  (1 + ω2)(1 + ω4)(1 + ω8)(1 + ω16) है

⇒ (1 + ω2 + ω4 + ω6)(1 + ω16 + ω8 + ω24)

⇒ (1 + ω2 + ω + 1)(1 + ω + ω2 + 1)     [(1) का उपयोग करके]

⇒ (0 + 1)(0 + 1)  [(2) का उपयोग करके]

⇒ 1

अतः, (1 + ω2)(1 + ω4)(1 + ω8)(1 + ω16) = 1

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