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Given a positive integer n a complex number z is called an n th root of unity if and only if zn 1.
N th root of unity math. N th roots of unity. Thus this equation has n roots which are also termed as the nth roots of unity. If a number is a root of unity then so is its complex conjugate. Mathematically if n is a positive integer then x is said to be an n th root of unity if it satisfies the equation x n 1.
If we denote the complex number by ω then therefore ω is an nth root of unity. 1 1 1 and 1 1 1 are the only real roots of unity. Using demoivre s theorem we find the nth roots of unity from the equation given below. N 1 2 3 is a number z satisfying the equation unless otherwise specified the roots of unity may be taken to be complex numbers including the number 1 and the number 1 if n is even which are complex with a zero imaginary part and in this case the n th roots of unity are.
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