![]() Ī new era in the theory of complex numbers and functions of complex arguments (analytic functions) arose from the investigations of L. Which describe the main characteristics of the complex number -the so-called modulus (absolute value), the real part, the imaginary part, and the argument. The last formula lead to the basic relations: Where is the distance between points and, and is the angle between the line connecting the points and and the positive -axis direction (the so-called polar representation). This geometric interpretation established the following representations of the complex number through two real numbers and as: The imaginary unit was interpreted in a geometrical sense as the point with coordinates in the Cartesian (Euclidean), ‐plane with the vertical -axis upward and the origin. Īccordingly, and and the above quadratic equation has two solutions as is expected for a quadratic polynomial: Gauss (1831) introduced the name "imaginary unit" for. Euler (1755) introduced the word "complex" (1777) and first used the letter for denoting. As a result, mathematicians proposed a special symbol-the imaginary unit, which is represented by : This problem was intensively discussed in the 16th, 17th, and 18th centuries. But it was not clear how to get –1 from something squared. It all started with questions about how to understand and interpret the solution of the simple quadratic equation. The study of complex numbers and their characteristics has a long history.
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