Find the value of |1-omega| where omega is cube root of unity.

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Solution

Dear Student,

$1, ω, ω^{2} a r e t h e c u b e r o o t s o f u n i t y ω = \frac{- 1 + i \sqrt{3}}{2}, ω^{2} = \frac{- 1 - i \sqrt{3}}{2} 1 + ω + ω^{2} = 0 ω^{3} = 1 S o, 1 - ω^{3} = 0 (1 - ω) (1 + ω^{2} + ω) = 0 A s, 1 + ω^{2} + ω = 0 & 1 - ω = 0 |1 - ω| = 0$

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