nombre_complexe.py

Created by edou559
Created on December 17, 2024
1001 Bytes
^=puissance
a`= conjugué de a 
^^= racine carrée
|= téta

1)forme algébrique:
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i^2 = -1

z = a+ib  -> z`= a-ib

2)forme trigonométrique:
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r(module) = (^^(a^2)+(b^2))
cos(|) = a/r
sin(|) = b/r

Propriété 1:
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arg(zz') = arg(z) + arg (z')
arg(z/z') = arg(z) - arg(z')

Propriété 2:
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(e^ia) * (e^ib) = e^i(a+b)
1/e^ia = e^-ia
(e^ia) / (e^ib) = e^i(a-b)
e^ian = (e^ia)^n
-1 = e^iPY
(e^ia)` = e^-ia

Propriété 3:
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cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

sin(a+b) = sin(a)cos(b)+sin(b)cos(a)
sin(a-b) = sin(a)cos(b)-sin(b)cos(a)

Propriété 4:
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cos(2a) = (cos(a))^2 - (sin(a))^2
Sin(2a) = 2sin(a)cos(a)

Propriété 5:
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(cos(a))^2 = 1/2(1+cos(a))
(sin(a))^2 = 1/2(1-cos(a))

Autre formule:
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(cos(x))^2 + (sin(x))^2 = 1

Si le cos est pair -> cos(-x) = cos(x)
Si le sin est impaire -> sin(-x) = -sin(x)