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The polynomial P(z) = [tex]z^{3} +mz^{2} +nz - 8[/tex] is divisible by (z+1+i), where z ∈C, m,n ∈R. Find the value of m and of n.

Respuesta :

Answer:

m=-2   n=-6

Step-by-step explanation:

(z+1+i)(z+1-i)=z²+2z+1-(i²)=z²+2z+2

z³+mz²+nz-8=(z²+2z+2)(z-4)=z³-2z²-6z-8

m=-2

n=-6

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