Answer: [tex]xy=-109i,[/tex]
and
[tex]\dfrac{x}{y}\dfrac{60}{109}+\dfrac{91}{109}i.[/tex]
Step-by-step explanation: We are given two complex numbers as follows :
[tex]x=10-3i,~~~~~y=3-10i.[/tex]
To find [tex]xy[/tex] and [tex]\dfrac{x}{y}.[/tex]
We have
[tex]xy\\\\=(10-3i)(3-10i)\\\\=30-9i-100i+30i^2\\\\=30-109i-30\\\\=-109i,[/tex]
and
[tex]\dfrac{x}{y}\\\\\\=\dfrac{10-3i}{3-10i}\\\\\\=\dfrac{(10-3i)(3+10i)}{(3-10i)(3+10i)}\\\\\\=\dfrac{30-9i+100i-30i^2}{9-100i^2}\\\\\\=\dfrac{30+91i+30}{9+100}\\\\\\=\dfrac{60+91i}{109}\\\\\\=\dfrac{60}{109}+\dfrac{91}{109}i.[/tex]
Thus,
[tex]xy=-109i,[/tex]
and
[tex]\dfrac{x}{y}=\dfrac{60}{109}+\dfrac{91}{109}i.[/tex]
