We shall now explain the result $$\cos \theta i\sin \theta = e^ = -1.$$ This proof uses differentialĮquations and it is not just an exercise in solving them. The most important mathematical constants in one formula In the nineteenth century Cauchy, Riemann and other mathematicians incorporated complex numbers into analysis thus extending the analysis of real numbers and giving complex numbers equal status. Gauss introduced the name complex numbers in 1832. Represented complex numbers as points in the plane. Without explaining his logic or identifying his dilemma, Heron bypassed the negation. Attempting to compute the volume of a truncated pyramid, he came across the expression (81-144), which produces the square root of a negative number, -63. Then Wessel (1797), Gauss (1800) and Argand (1806) all successfully Imaginary numbers almost appeared in the geometry of Heron of Alexandria in the first century A.D. Wallis (1616 - 1703) realised that real numbers could be represented on a line and made an early attempt to represent complex numbers as points in the plane. These so-called 'numbers' were treated with much suspicion by mathematicians for around another 200 years or so. Name gave rise to the term Cartesian coordinates. We call $x$ the real part and $y$ the imaginary part of the complex number and these terms were introduced by Descartes (1596 - 1650) whose Historically these numbers were thought of simply as mathematical tools useful in solving equations and called imaginary numbers. To follow up the idea that all the isometries are combinations of reflections, and to see how functions of a complex variable are used to work with transformations, see Footprints.
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