Pré-Vestibular ⇒ (MACK) Números Complexos: Forma Algébrica

[barbarahass]

Dado [tex3]f(z)=z^4+iz^3-(1+2i)z^2+3z+1+3i,[/tex3] o valor de [tex3]f[/tex3] no ponto [tex3]z=1+i[/tex3] é:

a) [tex3]1+i[/tex3]
b) [tex3]2+2i[/tex3]
c) [tex3]3+i[/tex3]
d) [tex3]7-i[/tex3]
e) [tex3]8+5i[/tex3]

Resposta:

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b

[Natan]

[tex3](1+i)^2=1+2i+i^2=1+2i-1=2i[/tex3]

• [tex3]\begin{array}{rl}
  f(1+i)&=[(1+i)^2]^2+i(1+i)^2(1+i) -(1+2i)(1+i)^2+3(1+i)+1+3i \\
  &=(2i)^2+2i^2(1+i) -2i(1+2i)+3+3i+1+3i \\
  &=-4 -2 -2i -2i -4i^2 +4 +6i \\
  &=2 + 2i
  \end{array}[/tex3]