1 Forme algébrique, forme trigonométrique

1 + i√3
√3 + i1 + i√3
1−i4
z1=√6 + i√2
2z2= 1 + i z3=z1 z2
z1, z2z3
cos 7π
12 sin 7π 12 
n∈N(1 + i)n
n∈N(1 + i)n+ (1 −i)n
z∈C|z−i|=|z+i|z
z z′zz′̸=−1
z+z′
1 + zz′
c∈C|c|<1.
z∈C,|z+c| ≤ |1 + cz| |z| ≤ 1.
D={z∈C||z| ≤ 1}C={z∈C||z|= 1}.
f:D→D, z 7→ z+c
1 + cz
f(C) = C.
acos x+bsin x.
a b r ∈R+t∈R
∀x∈R, a cos x+bsin x=rcos(x−t)
x∈Rcos x+ sin x= 1.
cos5(x) cos2(x) sin3(x)

n∈Nx∈R
n
k=0
cos(kx)
n
k=0
sin(kx)
z∈Cez= 3√3−3i
z1= 3 + 4i, z2= 8 −6i.
Z=√3 + i
cos π
12
1. z2−2iz −1+2i= 0 2. iz2+ (4i−3)z+i−5 = 0
3. z2−2z+ 1 = 0.
z∈Cz3+ (1 −3i)z2−(6 −i)z+ 10i= 0.
z0
z∈Cz3+ (1 −3i)z2−(6 −i)z+ 10i(z−z0)
z∈C
a. z3=−8i, b. z5−z= 0, c. 27(z−1)6+ (z+ 1)6= 0,
d. z2¯z7= 1, e. z6−(3 + 2i)z3+2+2i= 0.
z2=√2
2(1 + i) cos(π 8) sin(π 8)
w∈Cn1 1 + w+w2+···+wn−1= 0
a= cos(2π
5)b= cos(4π 5)s=a+b p =a·b
s p a b
n∈N r {0}
w n 1
n−1
k=0
(1 + wk)n
n1