complexe.py

Created on October 10, 2021
1.26 KB
Conversion 
0 30   45   60   90   180 360
0 pi/6 pi/4 pi/3 pi/2 pi  2pi
  
?*pi/180 radians
180*?/pi degre
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Tableau
x      0 pi/6      pi/4      pi/3      pi/2   pi 
sin(x) 0 1/2       sqrt(2)/2 sqrt(3)/2 1      0
cos(x) 1 sqrt(3)/2 sqrt(2)/2 1/2       0      -1
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Formule : 
module(r) = sqrt(a**2+b**2) 
arg = cos(a/r) et sin (b/r) 
Xp = module(p) * cos(p)
Yp = module(p) * sin(p)
cos0 = x/IzI 
sin0 = y/IzI
tan0 = y/x

Form alge= y=a+ib  cos(0)+isin(0)  i2=-1
Form exp  e**i0 * e**i0" = e**i(0+0")
(e**i0)**n = e**in0
e**i0/e**i0=e**i(0-0")   e**-i0=1/e**i0

Acos(wt+Q)= -Aw sin(wt+Q)
Asin(wt+Q)= Aw cos(wt+Q)

cos(0-0")=cos(0)cos(0")+sin(0)sin(0")
cos(0+0")=cos(0)cos(0")-sin(0)sin(0")
sin(0-0")=sin(0)cos(0")-sin(0)sin(0")
sin(0+0")=sin(0)cos(0")+cos(0)sin(0")
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Passer forme a l'autre : 
a+ib => e**i0
r=sqrt(a2+b2)
cos(a/r) sin(b/r)
= ?pi/? -> re**?pi/?

e**i0 => a+ib
e(cos(0)+isin(0))
= e(?+?i)
= e*?+e*?

x=IzI*icos(O en degre)
y=IzI*isin(O en degre)

IZ1+Z2I < ou = IZ1I + IZ2I
IZ1*Z2I = IZ1I * IZ2I
I1/Z1I = 1/Z1
IZ1/Z2I = IZ1I / IZ2I

arg(Z1+Z2) = arg(Z1)- arg(Z2)
arg(1/Z1)= -arg(Z1)
arg(Z1/Z2) = arg(Z1)- arg(Z2)
AB= IZB-ZAI
arg(Zb-ZA) = (u;AB)
(AB;AC)arg ZC-ZA / ZB-ZA