Abstract
It is frustrating that there is no \(x\in {\mathbb R}\) for which \(x^2=-1\). In this chapter we will introduce a structure that provides an extension of the real numbers in which this equation has solutions.
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Of course, thinking of \(\mathbb C\) in terms of \({\mathbb R}^2\), if \(z=x+iy\), then D(z, r) is the ball of radius r centered at (x, y). However, to emphasize that we are thinking of \(\mathbb C\) as the complex numbers, we will reserve the name disk and the notation D(z, r) for balls in \(\mathbb C\).
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© 2015 Springer International Publishing Switzerland
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Stroock, D.W. (2015). Elements of Complex Analysis. In: A Concise Introduction to Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-24469-3_2
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DOI: https://doi.org/10.1007/978-3-319-24469-3_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24467-9
Online ISBN: 978-3-319-24469-3
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