If a and B are complex cube root of unity then a^4 + a^-1 B^-1 + B4 =
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Solution
α and β are the complex cube roots of unity.
Hence,
α=ω,β=ω
2
Since,
⇒α
4
+β
4
+α
−1
+β
−1
⇒α
4
+β
4
+
α
1
+
β
1
⇒α
4
+β
4
+
αβ
α+β
Therefore,
⇒ω
4
+(ω
2
)
4
+
ωω
2
ω+ω
2
⇒ω+ω
8
+
ω
3
−1
⇒ω+ω
2
+
1
−1
⇒−1−1
⇒−2
Hence, this is the answer.
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