Question

Considere os seguintes números complexos Z1 = 4 + 2i ; Z2 = 5 – 4i calcule Z3 = /

Answer 1

Resposta:

Explicação passo-a-passo:

$z_3=\frac{z_1}{z_2}\\\frac{z_1}{z_2}=\frac{z_1}{z_2}\cdot\frac{\overline{z_2}}{\overline{z_2}}=\frac{z_1\cdot\overline{z_2}}{z_2\cdot \overline{z_2}}$

$\overline{z_2}=5+4i$

$z_1\cdot\overline{z_2}=(4+2i)\cdot(5+4i)=20+16i+10i-8=12+26i$

$z_2\cdot\overline{z_2}=25+16=41$

$z_3=\frac{z_1}{z_2}=\frac{z_1}{z_2}\cdot\frac{\overline{z_2}}{\overline{z_2}}=\frac{z_1\cdot\overline{z_2}}{z_2\cdot \overline{z_2}}=\frac{12+26i}{41}=\frac{12}{41}+\frac{26}{41}i$