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Let $\omega$ be a cube root of unity not equal to 1 . Then the maximum possible value of $\left|a+b w+c w^{2}\right|$ where $a$, b, $c \in\{+1,-1\}$ is
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$\left|a+b w+c w^{2}\right|$
$\quad|a-c+(b-c) w| \quad$, for maximum value taking $a=1, c=-1, b=1$
$\left|a+b w+c w^{2}\right|=|2+2 w|=2\left|w^{2}\right|=2$
$\quad|a-c+(b-c) w| \quad$, for maximum value taking $a=1, c=-1, b=1$
$\left|a+b w+c w^{2}\right|=|2+2 w|=2\left|w^{2}\right|=2$
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