Verified answer

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)