Question
Download Solution PDFयदि 1, ω, ω2 एकल के घन मूल हैं, तो (1 + ω) (1 + ω2) (1 + ω4) (1 + ω8) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
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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