MATH SOLVE

2 months ago

Q:
# if x=(10-3i) and y=(3-10i), then xy=? and x/y=?

Accepted Solution

A:

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: Β [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]