Question

ayudenme a simplificar esto -10-5i / -6+6i​

Answer 1

Respuesta:

$\frac{5}{12}+\frac{5}{4}i$

Explicación paso a paso:

$\mathrm{Aplicar\:la\:regla\:de\:aritmetica\:compleja}:\quad \frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}\:=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}}\\\\\\a=-10,\:b=-5,\:c=-6,\:d=6$

$\frac{-10-5i}{-6+6i}\\\\\frac{\left(-10\left(-6\right)+\left(-5\right)\cdot \:6\right)+\left(-5\left(-6\right)-\left(-10\right)\cdot \:6\right)i}{\left(-6\right)^2+6^2}\\\\\frac{10\cdot \:6-5\cdot \:6+\left(5\cdot \:6+10\cdot \:6\right)i}{\left(-6\right)^2+6^2}\\\\\frac{30+90i}{\left(-6\right)^2+6^2}\\\\\frac{30+90i}{36+36}\\\\\frac{30+90i}{72}=====>Factorizamos \\\\\frac{30\left(1+3i\right)}{72}==> Simplifica\\\\\frac{5\left(1+3i\right)}{12}\\\\\frac{5+15i}{12}$

$\frac{5}{12}+\frac{15i}{12} \\\\\frac{5}{12}+\frac{5}{4}i$