Question

P(x)=-x^4+3x^3-x^2-4x+1,sendo x=-i

Answer 1

Resposta:

P(x)=-x^4+3x^3-x^2-4x+1,sendo     x=-i

P(-i) =-(-i)⁴ +3 * (-i)³ -(-i)² -4*(-i)  + 1

P(-i) =-[(-1)⁴*i⁴] +3 * [(-1)³ *i³] -[(-1)²*i²] -4*(-i)  + 1

P(-i) =-i⁴ +3 * (-1) *i³ -i² +4i  + 1

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i=√(-1)

i²=[√(-1)]²=-1

i³=i*i²=-i

i⁴=i*i³=i*(-i) =-i²= 1

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P(-i) =-1 +3 * (-1) *(-i) -(-1) +4i  + 1

P(-i) =-1 +3i +1 +4i  + 1

P(-i) =3i +1 +4i  

P(-i) =1+7i