Question

(2+3i)/+4-5i) resolver​

Answer 1

Respuesta:

$=-\frac{7}{41}+\frac{22}{41}i$

Explicación paso a paso:

$\frac{2+3i}{4-5i}$

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

$=\frac{\left(2\cdot \:4+3\left(-5\right)\right)+\left(3\cdot \:4-2\left(-5\right)\right)i}{4^2+\left(-5\right)^2}$

$\mathrm{Simplificar}$

$=\frac{-7+22i}{41}$

$\mathrm{Reescribir\:}\frac{-7+22i}{41}\mathrm{\:en\:la\:forma\:binomica:\:}-\frac{7}{41}+\frac{22}{41}$

$=-\frac{7}{41}+\frac{22}{41}i$