Question

Sa se determine z ∈ C astfel incat z²+2z⁻+2=0
2z⁻=2z conjugat

Answer 1

fie z=a=bi, a, b∈R
atunci:

(a+bi)²+2a-2bi+2=0
a²-b²+2a+2+(2ab-2b)i=0+0i

a²-b²+2a+2=0
si
2b(a-1)=0


b=0 atunci a²-2a+2=0 a∉R
sau a=1
1-b²+2+2=0
b²=5 deci b=√5 sau b=-√5

deci z=1+i√5 sau z=1-i√5
se observa ca are 2 radacini complex conjugate


verificare (1+i√5)²+2-2i√5+2=1-5+2i√5+2-2i√5+2=0+0i
deci OK, numai verificam si pt conjugata
adevarat,  bine rezolvat