Question

Me ajudem, por favor!
Dividindo os números complexos Z = 6 + 2i por Z = 3 + 4i, qual é o resultado ?

Answer 1

$\large\boxed{\begin{array}{l}\sf Z_1=6+2i~~Z_2=3+4i\\\sf \dfrac{Z_1}{Z_2}=\dfrac{6+2i}{3+4i}\\\\\sf multiplicando~pelo~conjugado~do~denominador~temos\\\sf\dfrac{Z_1}{Z_2}=\dfrac{(6+2i)}{(3+4i)}\cdot\dfrac{(3-4i)}{(3-4i)}\\\\\sf \dfrac{Z_1}{Z_2}=\dfrac{18-24i+6i-8i^2}{3^2-(4i)^2}\\\\\sf \dfrac{Z_1}{Z_2}=\dfrac{18-24i+6i-8\cdot(-1)}{9-16\cdot(-1)}\\\\\sf \dfrac{Z_1}{Z_2}=\dfrac{26-18i}{25}=\dfrac{26}{25}-\dfrac{18}{25}i\end{array}}$