Question

Determina β ∈ C (multimea numerelor complexe) stiind ca ecuatia z³+(1+i)z²+iz+β=0 are solutia z1=1-i si rezolva ecuatia.

Answer 1

$(1-i)^2=1-2i+i^2=1-2i-1=-2i$
$(1-i)^3=-2i(1-i)=-2i+2i^2=-2i-2$
Inlocuim in ecuatie:

$-2i-2-2i+2+i+1+\beta=0\Rightarrow \beta=3i-1$