Abstract
There is no real number a for which \(\,a^{2} + 1 = 0\,\). In order to develop an expanded number system that includes solutions to this simple quadratic equation, we define the “imaginary number” \(\,i = \sqrt{-1}\,\). That is, this new number i is defined by the condition that \(\,i^{2} + 1 = 0\,\).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Feeman, T.G.: Conformality, the exponential function, and world map projections. Coll. Math. J. 32, 334–342 (2001)
Rudin, W.: Real and Complex Analysis, 2nd edn. McGraw-Hill, New York (1974)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Feeman, T.G. (2015). Complex Numbers. In: The Mathematics of Medical Imaging. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-22665-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-22665-1_4
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22664-4
Online ISBN: 978-3-319-22665-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)