Szczegółowe wyjaśnienie:
[tex]\dfrac{(5+i)(3+5i)}{i}=\dfrac{(5)(3)+(5)(5i)+(i)(3)+(i)(5i)}{i}\\\\=\dfrac{15+25i+3i+5i^2}{i}=(*)[/tex]
jeżeli [tex]i[/tex] to tylko jednomian, to:
[tex](*)=\dfrac{15+28i+5i^2}{i}}[/tex]
jeżeli [tex]i[/tex] to jednostka urojona, to:
[tex](*)=\dfrac{15+28i+5(-1)}{i}=\dfrac{15+28i-5}{i}=\dfrac{28i+10}{i}\cdot\dfrac{i}{i}=\dfrac{28i^2+10i}{i^2}\\\\=\dfrac{28\cdot(-1)+10i}{-1}=\dfrac{-28+10i}{-1}=28-10i[/tex]
[tex]i^2=-1[/tex]
