Nombres complexes - Maths Khalfallah

i2=−1C
a z
b z
z=a−ib
z
(O, −→ u;−→ v)
−→
u
−→
v
r=OM =|z|
b
a
θ
•M(a;b)z=a+b i
•z=a+b i M(a;b)
•z|z|OM |z|=√a2+b2
•z arg(z) (−→ u;−−→ OM)arg(z) = θ+ 2kπ
k= 0 k∈Zcos θ=a
√a2+b2sin θ=b √a2+b2
•z|z|arg(z) = θ
z=|z|(cos θ+isin θ)z= [r;θ]
∀M K TST I 2D2014−2015 2Ch8

z1= 4 −2i z2=−2−5i
z1+z2z1×z2
z1= 1 + i√3z2= 2 −2i
z r =|z|θ
z=reiθ z=|z|eiθ
θ θ0
eiθ ×eiθ0=ei(θ+θ0)
(eiθ )n=einθ
1
eiθ =e−iθ
eiθ
eiθ0=ei(θ−θ0)
eiθ =e−iθ
z=−2+2i
z1= 2e
i
π
3z2= 5e
i
π
4
z1×z2
z1
z2
∀M K TST I 2D2014−2015 2Ch8