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A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
An illustration of the complex plane. The imaginary numbers are on the vertical coordinate axis. Although the Greek mathematician and engineer Heron of Alexandria is noted as the first to present a calculation involving the square root of a negative number, [6] [7] it was Rafael Bombelli who first set down the rules for multiplication of complex numbers in 1572.
It was the first noncommutative division algebra to be discovered. According to the Frobenius theorem, the algebra is one of only two finite-dimensional division rings containing a proper subring isomorphic to the real numbers; the other being the complex numbers.
Hamilton also described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the "scalar" part, and the remaining three as the "vector" part. He coined the neologisms "tensor" and "scalar", and was the first to use the word "vector" in the modern sense.
In his work on the multivalued AGM of two complex numbers, he discovered a deep connection between the infinitely many values of the AGM to its two "simplest values". [134] In his unpublished writings he recognized and made a sketch of the key concept of fundamental domain for the modular group.
The concept of “infinity” appears simple at first glance, but becomes increasing more complex the more you think about it. Infinity means a never-ending sequence of numbers trailing off into ...
In mathematics, quaternions are a non-commutative number system that extends the complex numbers.Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, [1] but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space.
The simple number solves a notoriously complicated problem. For premium support please call: 800-290-4726 more ways to reach us