Respuesta :
Answer:
[tex]xy=-109i[/tex]
[tex]\frac{x}{y}=\frac{60}{109}+\frac{91}{109}i[/tex]
Step-by-step explanation:
[tex]xy=(10-3i)(3-10i)[/tex]
To compute x times y must use foil on the right hand side.
First: [tex]10(3)=30[/tex]
Outer: [tex]10(-10i)=-100i[/tex]
Inner: [tex]-3i(3)=-9i[/tex]
Last: [tex]-3i(-10i)=30i^2=-30[/tex]
------------------------------------Add like terms:
[tex]-109i[/tex]
----------------
[tex]\frac{x}{y}[/tex]
[tex]\frac{10-3i}{3-10i}[/tex]
Multiply top and bottom by bottom's conjugate:
[tex]\frac{(10-3i)(3+10i)}{(3-10i)(3+10i)}[/tex]
Foil the top and just do first and last of Foil for the bottom since the bottom contains multiplying conjugates:
[tex]\frac{30+100i-9i-30i^2}{9-100i^2}[/tex]
Replace [tex]i^2[/tex] with -1:
[tex]\frac{30+91i+30}{9+100}[/tex]
[tex]\frac{60+91i}{109}[/tex]
[tex]\frac{60}{109}+\frac{91}{109}i[/tex]
