Question

Sendo o ao quadrado =-1 dizer que 3/i+i/3 e igual a

Answer 1

$\dfrac{3}{i}+\dfrac{i}{3}=\dfrac{3\cdot3}{i\cdot3}+\dfrac{i\cdot i}{3\cdot i}\\\\\\\dfrac{3}{i}+\dfrac{i}{3}=\dfrac{9}{3i}+\dfrac{i^{2}}{3i}\\\\\\\dfrac{3}{i}+\dfrac{i}{3}=\dfrac{9+i^{2}}{3i}\\\\\\\dfrac{3}{i}+\dfrac{i}{3}=\dfrac{9+(-1)}{3i}\\\\\\\dfrac{3}{i}+\dfrac{i}{3}=\dfrac{8}{3i}\\\\\\\dfrac{3}{i}+\dfrac{i}{3}=\dfrac{8\cdot i}{3i\cdot i}\\\\\\\dfrac{3}{i}+\dfrac{i}{3}=\dfrac{8i}{3i^{2}}\\\\\\\dfrac{3}{i}+\dfrac{i}{3}=\dfrac{8i}{3(-1)}\\\\\\\boxed{\boxed{\dfrac{3}{i}+\dfrac{i}{3}=-\dfrac{8i}{3}}}$