The Complex Numbers

  • Daniel Rosenthal
  • David Rosenthal
  • Peter Rosenthal
Part of the Undergraduate Texts in Mathematics book series (UTM)


The polynomial x2 + 1 does not have any roots within the set of real numbers. A new number, called i, is introduced as a root of that polynomial. The complex numbers are all the numbers of the form a + bi where a and b are real numbers. It is a remarkable fact that every polynomial with real coefficients (or even with complex coefficients) that is not a constant function has a root within the set of complex numbers. In this chapter, we develop the basic properties of the complex numbers.

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Daniel Rosenthal
    • 1
  • David Rosenthal
    • 2
  • Peter Rosenthal
    • 3
  1. 1.TorontoCanada
  2. 2.Department of Mathematics and Computer ScienceSt. John’s UniversityQueensUSA
  3. 3.Department of MathematicsUniversity of TorontoTorontoCanada

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