Let ω be a cube root of unity not equal to 1. Then the maximum possible value of | a + b\omega + c\omega^2 | where a,b,c \in \{+1,-1\} is

KVPY SX SB Exam 2013 Question Paper

Question : 3 of 120

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Let ω be a cube root of unity not equal to 1. Then the maximum possible value of

| a + bω + cω^2 |

where

a,b,c ∈ \{+1,-1\}

Solution:

|a + bw + cw^2|

|a - c + (b- c)w|

, for maximum value taking a = 1 , c = -1, b = 1

|a + bw + cw^2|

= |2 + 2w|

= 2|w^2| = 2

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