The Complex Numbers. Trigonometric Sums. Infinite Products

  • Emanuel Fischer
Part of the Undergraduate Texts in Mathematics book series (UTM)


In order to solve the equation
$$a{x^2} + bx + c = 0,$$
where a, b, c are real numbers and a ≠ 0, for x ∈ ℝ, we use the identity
$$a{x^2} + bx + c = a\left[ {{{\left( {x + \frac{b}{{2a}}} \right)}^2} + \frac{{4ac - {b^2}}}{{4{a^2}}}} \right],$$
obtained by “completing the square.” A real number x satisfying (1.1) must satisfy
$${\left( {x + \frac{b}{{2a}}} \right)^2} = \frac{{{b^2} - 4ac}}{{4{a^2}}}.$$


Positive Integer Complex Number Nonnegative Integer Partial Product Infinite Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York, Inc. 1983

Authors and Affiliations

  • Emanuel Fischer
    • 1
  1. 1.Department of MathematicsAdelphi UniversityGarden CityUSA

Personalised recommendations