Сапунов Павел : другие произведения.

Complex numbers. The new (fourth) form of complex number

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   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 co
nnected 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 i x+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
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