XPost: rec.aviation.military   
   From: PointedEars@web.de   
      
   Jim Wilkins wrote:   
   > The square root of -1 is an interesting parallel.   
      
   A common misconception.  The imaginary unit is NOT defined as the square   
   root of −1.  Instead, the imaginary unit is defined such that its square is   
   equal to −1, so that it is a solution of the equation x² + 1 = 0.   
      
   IOW: ⅈ² := −1 ⇒ √(−1) = ±ⅈ.   
      
   > It has no apparent existence in our 3D Cartesian coordinates, yet its math   
   > describes an "imaginary" orthogonal 4th dimension of AC energy   
      
   Nonsense.   
      
   > in capacitance and inductance exquisitely well.   
   That this works has to do with Euler's formula:   
      
     exp(ⅈ φ) = cos(φ) + ⅈ sin(φ).   
      
     [One can see that this identity holds by writing it in terms of the Taylor   
      series of each function.]   
      
   It is thus possible to represent a point on a circle as a complex number,   
   and periodic quantities as complex numbers, especially those with constant   
   (angular) frequency:   
      
     φ(t) := ω t ⇒ exp(ⅈ ω t) = cos(ω t) + ⅈ sin(ω t).   
      
   F'up2    
      
   --   
   PointedEars   
      
   Twitter: @PointedEars2   
   Please do not cc me. / Bitte keine Kopien per E-Mail.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)