Nombres complexes - Dartmouth Math Home

z∈C<(z)=(z)|z|z¯z
C
U
n xn= 1
(ABM)z−a
z−b=e±iπ
3
z7−→ az +b
cos 6θsin 7θ θ
a∈C{z∈C|z¯z=a¯z+ ¯az}
(a, b)∈C×C∗Pn
k=0 cos(a+kb)
(a, b)∈C×C∗Pn
k=0 sin(a+kb)
(−4−2i)z2+ (7 −i)z+ 1 + 3i= 0
z4+6z3+17z2+24z+ 52 = 0
θ∈[0,2π[
z2−(2θ+1 cos θ)z+ 22θ= 0
A B θ (ABO)
h:C\ {2i} −→ Cz7−→ z+1
z−2iM
z
h(z)∈R
h(z)∈iR
arg(h(z)) = π
2
z=5+i√3
2−i√3z M0
z0(OMM0)
A B C a b c |a|=|b|=|c|
(ABC)a+b+c= 0
n(1 + i)n∈R

x+i
x−i, x ∈R=S1\ {1}
ω= cos 2π
5+isin 2π 5α=ω+ω4β=ω2+ω3
1 + ω+ω2+ω3+ω4= 0
α β X2+X−1 = 0
αcos 2π
5ω.ω 4
cos 2π
5