Complex numbers. The new (fourth) form of complex number
At first I it in any way did not name... But has then understood: long so cannot proceed. And then I it named so: "the Compact form of complex number", as it really compact. Here it:
vix
cannot be more compactly... v is a module комлексного numbers i is imaginary unit x is an argument Most conveniently to compare the compact form to the indicative. If two numbers are equal each other:
vix = meiz
That modules of compact and indicative forms are equal: v = m and arguments are connected by the formula:
x = z / (0.5 C)
Where C = 3,14159... (Number of Pifagora)
That is the argument is measured not in radians, and in quarters that is clear from drawing:
The numbers which have been written down in the compact form, it is possible to multiply and put:
vix w iy = vw ix+y
I here will not result the formula of addition: it is a little bulky.
There are also other useful consequences. Instead of Euler's formula it is possible to write:
cos (x C/2) = 0.5 ix + 0.5 i-x
Certainly, only when such record gives any benefit at the decision of any specific target.
Pavel Sapunov
Moscow
11 March 2008
sapunovpavel@rambler.ru