Mathematics which is useful for making sense of things, and how they
are used. On the history of Complex numbers, the plan d'Argand - adding
Geometry to the Cartesian plane -is really quite clever. As explained in Film 5
of the Dimensions series, once one has the courage to leave the numbers line,
and express things using i, the figures formed can be used to compute
using vector-like computational techniques. (Vectors themselves will come later,
because as well as a orientation and magnitude, a proper vector has a direction).
Euler eventually adopted the Argand plane as well. Euler's Formula states that any
real number can be expressed on this plane. Indeed it can, because in Polar
notation, the coefficient of pi makes one jump back and forth on the line, while
the r value is the modulus ie the magnitude.
notation, the coefficient of pi makes one jump back and forth on the line, while
the r value is the modulus ie the magnitude.
An interesting aside, the idea of the complex number plane was first put
forward by John Wallis in the 17th Century. He taught Geometry at Oxford
University at a time when Oliver Cromwell was Chancellor (De Algbra
Tractacus, 1685).
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