mathspe.py

Created on November 28, 2021

519 Bytes

forme algébrique
i2=-1 zbarre=a-ib z*zbarre=a2+b2
z'/z=z'*zbarre/z*zbarre
zbarre= conjugué de z
ex: 
z=2+3i  z'=-5+i
2z-3z'=(2*2+3i)-(-3-5+1)=19+3i
z*z'=(2+3i)(-5+i)=-13-3i
conjugué z+z'= conj -3+4i=-3-4i
z/z'=2+3i/-5+i=-7-17i/26

forme trigo
module z=r=sqrt(a2+b2)
module z2=z*zbarre
arg(z)=teta=
cos(teta)=a/r
sin(tet)=b/r
z=rcos(teta)+isin(teta)

      cos       sin
0     1         0
pi/6  sqrt(3)/2   1/2
pi/4  sqrt(2)/2   sqrt(2)/2
pi/3  1/2       sqrt(3)/2 
pi/2  0         1
pi    -1        0

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