From: retenshun@gmail.com   
      
   to be honest my refresher but if it help i'm happy.   
      
   "Trigonometry"   
      
    e^(iwt) = cos(wt) + isin(wt)   
      
    i^2 = -1 and i = squareroot(-1).   
      
   2(i)sin(wt) =    [e^(iwt) - e^(-iwt)].   
      
   2cos(wt) = [e^(iwt) + e^(-iwt)].   
      
   2sinh(wt) = [e^(-i(iwt)) - e^(i(iwt))] = [e^(wt) - e^(-wt)]= 2sin(-iwt)) =   
   -2sin(iwt).   
      
   2cosh(wt) = (e^(-i(iwt)) + e^(i(iwt))) = (e^(wt) + e^(-wt)) = 2cos(iwt).   
      
   Further identities and such can be easier if   
      
   e^(iwt) = cos(wt) + isin(wt) is used instead of your noodle.   
      
   an aside I found  interesting: e^(irwt) = cos(rwt) + isin(rwt) = (cos(wt) +   
   isin(wt))^r.   
      
   "polar notation".   
      
    "(angle)" being that similar to "<" or "L" is  a character I'd rather not   
   render here.   
      
   let  s = x + iy where x and y real.   
      
   R (angle) theta = |square root(x^2 + y^2)| (angle) (tan^(-1)(y/x)).   
      
   If x = cos(wt) and y = sin(wt) that if s = e^(iwt) = x + iy = cos(wt) +   
   isin(wt)   
      
   then R (angle) theta = 1 (angle) (wt).   
      
    Also, the absolute value of s is denoted as |s|. |s| >=0 and is real.   
      
   |s| = | [(x + iy)(x -iy)]^(1/2) |  = |sqt(x^2 + y^2)| = |sqr(s(s*))|.   
      
   s* = x - iy is always the 'complex conjugate' of s = x + iy.   
      
   In electrical engineering they often use 'j' for sqr(-1) instead of 'i' as 'i'   
   is used as a variable for small signal current.   
      
   "A sinusoidal voltage"   
      
   A sinusoidal voltage can be represented as V_p(e^(jwt)) where V_p is the real   
   part and is actually the peak voltage of the waveform.   
      
   "Passive circuits with a steady state sinusoidal volatge"   
      
   Ususally Root Mean Square of a Voltage, V_rms = V  is used.   
      
   Under these conditions V_rms(angle)wt is simplified to V == V_rms = V_p /   
   sqr(2).   
      
   please note w = 2(pi)f where f is the frequaency in units of cycles per second   
   or just 1/seconds called  Hertz   
      
   and w is "radians per second".   
      
    "Passive components"   
      
    "Impedance, Z"   
      
   Z = R is the the impedence of a resitor, R, usually in units of Ohms.   
      
   note: 1/Ohm(s)  is a "mho", funny eh?   
      
   Z = 1/(jwC) is the impedence  of a capacitor,  C,  usually in units of Farads.   
      
   Z = jwL  is the impedance of an inductor, L,  usually in units of Henries.   
      
   I(angle)(phi) = V/Z.  Where Z is in a simple a loop with V.   
      
      
   phi is the relative phase compared with V being 0 degrees.   
      
   phi = 90 degrees = pi/2 if the load, Z, is purely capacative.   
      
   phi = -90 = -pi/2 if the load, Z , is purely inductive.   
      
   phi = 0 if the load, Z, is purely resistive.   
      
      
   We can analyse these notions using a graph  with an x-axis  and a y-axis. For   
   instance jwL   
   falls of the y-axis (the imaginary axis) and therefore forms a 90 degree angle   
   with the x- axis (the real axis) as this is the standard convention.   
      
   "total impedance, Z_t"   
      
   Z_t = Z_1 + Z_2 + .... + Z_n   
      
   if all Z_i  on the right hand side of this equation are in series in the   
   circuit.   
      
   Z_t = 1 /  (1/Z_1 + 1/Z_2 + ... + 1/Z_m ) or 1/Z_t = (1/Z_1 + 1/Z_2 + ... +   
   1/Z_m )   
      
   if all Z_i on the right hand side of the equation(s) are in parallel in the   
   circcuit.   
      
   And any passive circuit can be usually be reduced ultimatly to a load of   
   impedance, Z,  in a simple loop both parallel and in series with the voltage   
   V, being a steady stae sinusoid.   
      
   Simon Roberts (I had forgot these,  it is not all be clearly written, I know)   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)