Phillips Nunez
05/20/2024 · Middle School
Exercice \( \mathbf{1}: \mathbf{8} \) pts On considère dans l'ensemble \( C \) l'équation (E) suivant : (E) \( z^{3}-(2+3 i) z^{2}+2(5+3 i) z-20=0 \) l) montrer que l'équation ( E\( ) \) admet deux solutions imaginaires pures à déterminer 2) Déterminer le nombre complexe u pourque l'équation (E) s'écrive sous la forme (z+2i) \( (z-5 i)(z+u)=0 \) 3) en déduire la résolution dans C de l'équation \( (\mathrm{E}) \)
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1) Les solutions imaginaires pures sont \( z_1 = 5i \) et \( z_2 = -2i \).
2) \( u = -2 \).
3) Les solutions de l'équation sont \( z = -2i, \quad z = 5i, \quad z = -2 \).
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