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Nyx
a fost răspuns

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

Răspuns :

[tex](1-i)^2=1-2i+i^2=1-2i-1=-2i[/tex]
[tex](1-i)^3=-2i(1-i)=-2i+2i^2=-2i-2[/tex]
Inlocuim in ecuatie:

[tex]-2i-2-2i+2+i+1+\beta=0\Rightarrow \beta=3i-1[/tex]

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