Question

efectua y simplifica
$- (3 - i) \div (5 - i)$
​

Answer 1

Respuesta:

$=-\frac{8}{13}+\frac{1}{13}i$

Explicación paso a paso:

$-\frac{3-i}{5-i}\\\\\mathrm{Aplicar\:la\:regla\:de\:aritmetica\:compleja}:\quad \frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}\:=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}\\\\a=3,\:b=-1,\:c=5,\:d=-1\\\\=-\frac{\left(3\cdot \:5+\left(-1\right)\left(-1\right)\right)+\left(-1\cdot \:5-3\left(-1\right)\right)i}{5^2+\left(-1\right)^2}\\\\\mathrm{Simplificar}\\\\=-\frac{16-2i}{26}$

$\mathrm{Simplificar}\:-\frac{16-2i}{26}:\quad -\frac{8-i}{13}\\\\=-\frac{8-i}{13}\\\\\mathrm{Reescribir\:}-\frac{8-i}{13}\mathrm{\:en\:la\:forma\:binomica:\:}-\frac{8}{13}+\frac{1}{13}i\\\\=-\frac{8}{13}+\frac{1}{13}i$