Question

qual é o conjugado de z=(2+i)/(7-3i)?

Answer 1

$z=\dfrac{2+i}{7-3i}$

Conjugado de 7 - 3i ---> 7 + 3i

Multiplicando o numerador e o denominador pelo conjugado do denominador:

$z=\dfrac{(2+i)(7+3i)}{(7-3i)(7+3i)}\\\\\\z=\dfrac{14+6i+7i+3i^{2}}{7^{2}-(3i)^{2}}\\\\\\z=\dfrac{14+13i+3(-1)}{49-9i^{2}}\\\\\\z=\dfrac{14+13i-3}{49-9(-1)}\\\\\\z=\dfrac{11+13i}{49+9}\\\\\\z=\dfrac{11+13i}{58}\\\\\\\boxed{\boxed{z=\dfrac{11}{58}+\dfrac{13}{58}i}}$

Tendo a forma algébrica do número, podemos achar seu conjugado:

$\boxed{\boxed{\overline{z}=\dfrac{11}{58}-\dfrac{13}{58}i}}$