Question

4)   Com os três números complexos do exercício nº 3, calcule: ​

Answer 1

O valor da expressão dada é -44.

Explicação

Do exercício 3, sabemos que $\mathsf{z_1=1+5i,\,z_2=-4+2i}$ e $\mathsf{z_3=5.}$

Dessa forma, segue que:

$\large\mathsf{z_3\cdot z_2+\overline{z^{2}_1}=}\\\\\\\large\mathsf{=5\cdot(-4+2i)+\overline{(1+5i)^2}=}\\\\\\\large\mathsf{=-20+10i+\overline{1^2+2\cdot 1 \cdot 5i+(5i)^2}=}\\\\\\\large\mathsf{=-20+10i+\overline{1+10i-25}=}\\\\\\\large\mathsf{=-20+10i+\overline{-24+10i}=}\\\\\\\large\mathsf{=-20+10i+(-24-10i)=}\\\\\\\large\mathsf{=-20+10i-24-10i=}\\\\\\\large\mathsf{=-44}$

Logo,

$\large\boxed{\mathsf{z_3\cdot z_2+\overline{z^{2}_1}=-44.}}$

Dúvidas? Comente.