Français des mathématiques - Plate

3+4i
1−i(2 + i)3i2006 i+1 i
z2+ (i−5)z+26+2i= 0
z4+ 6z3+ 9z2= 0 z4+ 6z3+ 9z2+ 100 = 0
j=−1
2+i√3 2
j2=j
1 + j+j2j3= 1
n∈N
(1 + 1)n(1 + j)n(1 + j2)n
C0
n+C3 n+C6 n+· · · +C3k n+· · · =2n+ 2 ·(−1)n·jn
3.
n∈NC0
n+C3 n+C6 n+· · · +C3k n+· · · 2n
3
z|z+iz|62|z|
z
a, b, c, d ad −bc > 0
zaz+b
cz+d
a, b, c, d a, b, c
X=d−a
b−c, Y =d−b c−a, Z =d−c a−b.
X, Y, Z
X=Y= 0 d−a=ik(b−c)d−b=il(c−a)k l

o
eiθ θ
o
n
z zn= 1
z zn= 1 n
n= 6 n
α β n α ·β α 1
αn
n n
o
1 + i−1−2iπ
32
o
cos3θcos 3θ, cos θsin3θsin 3θ, sin θ
cos3θsin3θ
o
z+ 2z+i= 0
eiθ z+e−iθ z= 1
|z−i|<1
ez= 1
o
cos 5θcos θ
o
z z, z2, z5
o
z=a+ib ez
o
w∈Cz ez=w
z1z2z1−z2
z ez= 0