Question

Calcule quociente de 3+4i por 4-3i

Answer 1

$Como\;\; \dfrac{a+bi}{c+di}\:=\:\dfrac{\left(a+bi\right)\left(c-di\right)}{\left(c-di\right)\left(c+di\right)}\:\\\\ \\ \dfrac{3+4i}{4-3i} = \dfrac{(3+4i)(4-3i)}{(4+3i)(4-3i)} \\\\ \\ \dfrac{\left(3\cdot \:4+4\left(-3\right)\right)+\left(4\cdot \:4-3\left(-3\right)\right)i}{4^2+\left(-3\right)^2}\\\\ \\ \dfrac{25i}{25} = i$