Find the real numbers `x\ a n d\ y ,` if `(x-i y)(3+5i)` is the conjugate of `-6-24 idot`

Options

A. `x=3 and y=3`
B. `x=3 and y=-3`
C. `x=-3 and y=-3`
D. none of these

Answer

B

Explanation

According to the problem,
`(x-iy)(3+5i)=bar((-6- 24i))`
`" "=-6+ 24i`
`rArr" "x-iy =(-6+24i)/(3+5i)`
`" "=(-6+ 24i)/( 3+5i)xx(3-5i)/(3-5i)`
` " "=(-18+ 30i+ 72i-120i^(2))/(9-25i^(2))`
`" "=(102+ 102i)/(34)`
`" "=3+ 3i`
` therefore" "x=3 and y=-3`