2.8.3 The n th roots of unity
Chapter 2: Chapter 2 · MATHEMATICS-VOLUME 1 · EN medium
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The solutions of the equation z n = , for positive values of integer n , are the n roots of the unity. In polar form the equation z n = can be written as n = ) + π = e i k p , k = , , , . Using De Moivre’s theorem, we find the n th roots of unity from the equation given below: e i k + = , , , , . … ( ) Given a positive integer n , a complex number z is called an n th root of unity if and only if z n = . If we denote the complex number by ω , then ω = e ⇒ ω n = e e . Fig. . Re Im
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 95
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The solutions of the equation z n = , for positive values of integer n , are the n roots of the unity. In polar form the equation z n = can be written as n = ) + π = e i k p , k = , , , . Using De Moivre’s theorem, we find the n th roots of unity from the equation given below: e i k + = , , , , . … ( ) Given a positive integer n , a complex number z is called an n th root of unity if and only if z n = .
If we denote the complex number by ω , then ω = e ⇒ ω n = e e . Fig. . Re Im
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