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If z is an nth root of 1, 1/z is too

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If z is an nth root of one, meaning it satisfies the equation z^n = 1, then 1/z must also be an nth root of one. Complex roots of equations with natural coefficients always exist in conjugate pairs, so if z is a root, then 1/z is also a root, satisfying the same equation z^n = 1.

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Show that if "z" is an "n-th" root of one, then so is 1/z Solution we know that when z is a complex number and is a root of an equation which has natural coefficients , then the complex roots always exist in conjugate pairs , so if Z is a root , then 1/Z should also be a root of the given equation i.e n-th root of 1 .

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If z is an nth root of 1, 1/z is too

  • 1. Show that if "z" is an "n-th" root of one, then so is 1/z Solution we know that when z is a complex number and is a root of an equation which has natural coefficients , then the complex roots always exist in conjugate pairs , so if Z is a root , then 1/Z should also be a root of the given equation i.e n-th root of 1 .