Let w  = 1 be a cube root of unity. Possible value(s) of ( 1 − w + w 2 ) ( 1 − w 2 + w 4 ) … .. ( 1 − w n + w 2 n ) ; where n ∈ N , is/are

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For n = 3 K , we have S = 2 3 2 n ​ . For n = 3 K + 1 : 1 − w n + w 2 n = − 2 w ⇒ S = − 2 2 ⌊ 3 n ​ ⌋ + 1 For n = 3 K + 2 : 1 − w n + w 2 n = − 2 w 2 ⇒ S = 2 2 ⌊ 3 n ​ ⌋ + 2 B n

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JEE Advanced (2028)