Multivalued Functions, Branch Points, and Cuts

Harold Cohen ()
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Harold Cohen: California State University, Los Angeles, Department of Physics and Astronomy

Chapter Chapter 6 in Complex Analysis with Applications in Science and Engineering, 2007, pp 165-223 from Springer

Abstract: Abstract Because ei2π = 1, it is straightforward to see that if the argument of a complex variable z is increased by 2π, one obtains the same value of the complex variable. That is, for a given r and θ, we write (6.1a) $$ z(r,\theta ) = re^{i\theta } $$ Then (6.1b) $$ z(r,\theta + 2\pi ) = re^{i\theta } e^{2i\pi } = re^{i\theta } = z(r,\theta ) $$

Keywords: Real Axis; Branch Point; Multivalued Function; Root Function; Positive Real Axis (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-0-387-73058-5_6

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