One way of viewing imaginary numbers is to consider a standard number line positively increasing in magnitude to the right and negatively increasing in magnitude to the left. Geometrically, imaginary numbers are found on the vertical axis of the complex number plane, which allows them to be presented perpendicular to the real axis. In 1843, William Rowan Hamilton extended the idea of an axis of imaginary numbers in the plane to a four-dimensional space of quaternion imaginaries in which three of the dimensions are analogous to the imaginary numbers in the complex field. The geometric significance of complex numbers as points in a plane was first described by Caspar Wessel (1745–1818). The use of imaginary numbers was not widely accepted until the work of Leonhard Euler (1707–1783) and Carl Friedrich Gauss (1777–1855). Many other mathematicians were slow to adopt the use of imaginary numbers, including René Descartes, who wrote about them in his La Géométrie in which the term imaginary was used and meant to be derogatory. At the time, imaginary numbers and negative numbers were poorly understood and were regarded by some as fictitious or useless much as zero once was. The concept had appeared in print earlier, such as in work by Gerolamo Cardano. The imaginary numbers are on the vertical coordinate axis.Īlthough the Greek mathematician and engineer Hero of Alexandria is noted as the first to have conceived imaginary numbers, it was Rafael Bombelli who first set down the rules for multiplication of complex numbers in 1572. Originally coined in the 17th century by René Descartes as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century).Īn imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number. By definition, zero is considered to be both real and imaginary. For example, 5 i is an imaginary number, and its square is −25. The square of an imaginary number bi is − b 2. For the 2013 EP by The Maine, see Imaginary Numbers (EP).Īn imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2 = −1. In addition, we offer supportive therapies, suchĪs gut-directed hypnotherapy, to relieve troubling symptoms in certain patients."Imaginary Numbers" redirects here. Our GI physiology laboratory provides 24-hour monitoring for gastroesophageal reflux, motility studies of the esophagus, sphincter of Oddi and rectum, and evaluation SLUCare providers are also experts in treating pancreatitis, pancreatic cancer, inflammatory bowel disease and motility disorders. Learn About Colonoscopy Screenings with SLUCare Procedures, including upper endoscopies, colonoscopies, and liver biopsies, as well as specialized treatment for diseases of the stomach, liver, small intestine
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