Bonjour,
1)
(2-i)²+2i(2-i)= 4-1-4i+4i-2=1 : A∈E
(-i)²+2i(-i)=-1+2=1: B∈E
2)z=x+iy
z'=x'+iy'
z'=z²+2iz
x'+iy'=(x+iy)²+2i(x+iy)
=x²-y²+2ixy+2ix-2y
==> x'=x²-y²-2y
y'=2xy+2x
3)
E={x'+iy'=r | r∈R}
==>x²+y²-2y=r et (2xy+2x=0 ou 2x(y-1)=0)
==> x=0 et (y²-2y+1=+1 ou (y=-1 +√(r+1) ou y=-1-√(r+1) ==> r>=-1)
ou
y=-1 et (x²=r-3 ==>r>=3)
