QCM nombres complexes corrigé math analyse numérique licence
QCM
Nombres
complexes
Q
u
e
s
t
i
o
n
1
Le
nombre
complexe
1
+
i
3
1
−
i
20
v
a
u
t
:
□
2
9
□
i
2
9
□
2
9
1
+
i
3
☑
2
9
1
−
i
3
Q
u
e
s
t
i
o
n
2
Soit
u
racine
5
i
è
me
de
l
'
u
n
i
t
é
et
u
≠
1
,
alors
1
+
u
+
u
2
+
u
3
est
é
gale
:
□
1
u
☑
−
1
u
□
1
u
−
1
□
1
u
+
1
Q
u
e
s
t
i
o
n
3
∑
k
=
1
10
sin
2
k
π
7
+
icos
2
k
π
7
est
é
g
a
l
e
:
□
1
□
−
1
□
i
☑
−
i
Q
u
e
s
t
i
o
n
4
le
module
du
nombre
complexe
Z
=
2
+
i
5
2
−
i
5
10
+
2
−
i
5
2
+
i
5
10
v
a
u
t
:
☑
2
c
o
s
20
arcos
2
3
□
2
s
i
n
20
arcos
2
3
□
2
c
o
s
10
arcos
2
3
□
20
cos
2
arcos
2
3
Q
u
e
s
t
i
o
n
5
la
partie
r
é
elle
du
nombre
comple
ω
=
1
−
cos
θ
+
2
i
s
i
n
θ
−
1
est
é
g
a
l
e
:
□
1
3
+
5
c
o
s
θ
☑
1
5
+
3
c
o
s
θ
□
1
3
−
5
c
o
s
θ
□
1
5
−
3
c
o
s
θ
Q
u
e
s
t
i
o
n
6
Soit
ω
le
point
d
'
a
f
f
i
x
e
i
.
L
'
e
x
p
r
e
s
s
i
o
n
complexe
du
rotation
de
centre
ω
et
d
'
a
n
g
l
e
π
2
est
☑
z
'
=
iz
+
1
+
i
□
z
'
=
−
iz
+
1
+
i
□
z
'
=
iz
−
1
+
i
□
z
'
=
iz
+
1
−
i
Q
u
e
s
t
i
o
n
7
On
considere
le
nombre
complexe
ω
=
2
3
e
2
i
π
3
,
on
pose
α
n
=
ω
n
+
1
−
ω
n
Alors
on
a
:
☑
α
n
=
19
3
2
3
n
□
α
n
=
2
3
n
+
1
−
2
3
n
□
α
n
=
15
13
2
3
n
□
α
n
=
13
15
2
3
n
□
α
n
=
3
19
2
3
n
Question
8
Soit
I
le
po
int
d
'
affixe
3
i
.
L
'
ensemble
des
po
int
s
d
'
affixes
z
telque
iz
+
3
z
−
3
i
=
1
est
:
□
l
'
axe
des
abscisse
.
□
l
'
axe
des
ordonn
é
es
priv
é
du
po
int
I
.
□
une
cercle
de
rayon
1
priv
é
e
du
po
int
I
.
☑
le
plan
priv
é
du
po
int
I
.
Question
9
On
pose
S
=
1
+
2
ω
0
+
3
ω
2
0
+
...
+
n
ω
0
n
−
1
avec
ω
0
est
la
racine
ni
è
me
de
l
'
unit
é
.
S
vaut
alors
:
□
S
=
1
ω
0
−
n
□
S
=
n
ω
0
−
n
□
S
=
1
ω
0
−
1
☑
S
=
n
ω
0
−
1
Question
10
−
1
+
−
3
2
3
n
+
−
1
−
−
3
2
3
n
vaut
:
□
−
1
□
1
☑
2
□
3
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