Question

If w is a non-real cube root of unity, then the value of

(3+w + 3w²)+ is

(a)16

(b)16 w

(c)16 w²

(d) –16 w​

Answer 1

Step-by-step explanation:

We know,

ω3=1

1+ω+ω2=0

Now,

(3+5ω+3ω2)2+(3+3ω+5ω2)2

⇒ −3ω+5ω)2+(−3w2+5ω2)2           [ Since, 1+ω2=−ω ]

⇒  (2ω)2+(2ω2)2

⇒  4ω2+4ω4

⇒  4(ω+ω2)                                  [ ω4=ω.ω3=ω ]

⇒  4(−1)                                         [ ω+ω2=−1 ]

⇒  −4

∴   (3+5ω+3ω2)2+(3+3ω+5ω2)2=−4

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