TD 1. Révisions : nombres complexes, séries, topologie

i−1 + i√3√2e−iπ/4
z→z+i z →iz z →2z z →(−1 +
i√3)z
x∈R
n
X
k=0
sin(kx).
znzn/(1−zn)z∈C
un
un+1/unl u1/n
nl
vn0un
Punvn
vnθ∈R\2πZ
s
X
k=q+1
vkeikθ
≤vq+1
|sin(θ/2)|.
PunPvn
wn=
n
X
k=0
ukvn−k.
PwnX
n
unX
k
vk
R R
R C
z∈C\S1
zn−1
zn+ 1
n→+∞f(z)f
C
CR2[(0,−1),(0,1)]
x7→ sin(1/x)x > 0C
F p RnRn\F