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If ω is a complex cube root of unity, then prove the following: (ω2 + ω - 1)3 = – 8 - Mathematics and Statistics

Sum

If ω is a complex cube root of unity, then prove the following: (ω2 + ω - 1)3 = – 8

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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
L.H.S. = (ω2 + ω - 1)3
= (– 1 – 1)3
= (– 2)3
= – 8 = R.H.S.

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 5. (i) | Page 42
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