Question

Dado o polinômio P(x)=x²-2x+1,sendo i√-1,calcular
A)P(i)
B)P(1+i)
C)(2-3i)

Answer 1

OBS.: $i^{2} = \sqrt{ (-1)^{2} } =-1$

A)

$P(i)= i^{2} -2i+1 \\ P(i)= -1 -2 i+1 \\ P(i)=-2i$

B)

$P(1+i)= (1+i)^{2} -2(1+i)+1 \\ P(1+i)= 1+2i+ i^{2} -2-2i+1 \\ P(1+i)= 1-1 -2+1 \\ P(1+i)= -1$

C)

$P(2-3i)= (2-3i)^{2} -2(2-3i)+1 \\ P(2-3i)= 4-12i+9i^{2}-4+6i+1 \\ P(2-3i)= -12i+9(-1)+6i+1 \\ P(2-3i)= -6i-8$