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Gauss definition as Complex Number: x + yi (where x and y are real numbers and y is an imaginary unit) - Gauss results and reputation settled the acceptance of imaginary numbers. ▓ Imaginary numbers were defined in 1572 by Rafael Bombelli  many people believed they were fictitious during this time period. Even Descartes was slow to believe. He wrote about them in his La Gщomщtrie, where the term was meant to be derogatory.╣ Viete also did not accept negative numbers and imaginary numbers.▓ Descartes was the first to use the term  imaginary number in 1637. However, imaginary numbers were invented much earlier by Gerolamo Cardano in the 1500s but they were not widely accepted until the work of Leonhard Euler (1707 1783) and Carl Friedrich Gauss (1777 1855).╣ Euler introduced the letter i for "-1 in 1748.▓ Caspar Wessel used "-1 = ╡ in 1797.╣ Myth: A negative number is not a square.╣ (A nega- tive x a negative is a positive, there is not number times itself that will give you a negative value, therefore, how can you take the square root of a negative number?) Example: -5 x -5 = 25 5 x 5 = 25 therefore " 25 = ▒5 "-25 - there is no number times itself that will give you -25 Bombelli continued Cardano s work╣ x▓ + a = 0 solutions: + "a and - "-a x▓ + 1 = 0, then x▓ = -1 and x = ▒"-1 i = "-1, then i▓ = -1 i│ = - "-1 i4 = 1 i5 = "-1 Albert Girard (1629)  By using Imaginary Numbers, it shows that an equation can have many roots as its degree.▓ Showed x 4 4x + 3 = 0 Has Roots: 1, 1, -1 + "2, and -1 - "2 Leonhard Euler (18th century) Proved the Formula: e2└i = 1 Biography ╣ http://en.wikipedia.org/wiki/Imaginary_number ▓ Baumgart, John K., Historical Topics for the Mathematics Classroom. VA. National Council of Teachers of Mathematics, INC, 2006 Do Imaginary Numbers Really Exist? 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