Abstract
A complex number of unit modulus (r=l) is of the form exp iθ or cos θ+i sin θ, where θ is real. In the z-plane these points are represented by the points on the circumference of the unit circle x 2 +y 2=1. Note that the condition zz̄=1 is equivalent to z̄=z -1, so that complex numbers of unit modulus are characterized by the fact that the conjugate complex coincides with the reciprocal.
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© 1962 Walter Ledermann
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Ledermann, W. (1962). Roots of Unity. In: Complex Numbers. Library of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-6570-9_3
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DOI: https://doi.org/10.1007/978-94-011-6570-9_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7100-4345-0
Online ISBN: 978-94-011-6570-9
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