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If ω is a complex cube root of unity, find the value of ω2 + ω3 + ω4. - Mathematics and Statistics

Sum

If ω is a complex cube root of unity, find the value of ω2 + ω3 + ω4.

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Solution

ω is a complex cube root of unity
∴ ω3 = 1 and 1 + ω + ω2 = 0

Also, 1 + ω2 = - ω, 1 + ω = -  ω2 and ω + ω2 = – 1

ω2 + ω3 + ω4

= ω2 (1 + ω + ω2) = ω2(0) = 0 

Concept: Concept of Complex Numbers - Cube Roots of Unity
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Exercise 3.3 | Q 2. (ii) | Page 42
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