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Find the real numbers x and y , if (x-i ...

Find the real numbers `x and y ,` if `(x-i y)(3+5i)` is the conjugate of `-6-24 i`

A

` x = -2, y=2`

B

` x = -3, y=3`

C

` x = 3, y=-3`

D

` x = -4, y=1`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `z = (x-iy) (3+5i)`
`=3x + 5xi - 3yi - 5yi^(2)`
`= (3x + 5y)+i(5x -3y)`
`therefore barz = (3x + 5y) - i(5x - 3y)`
It is given that ,`barz = - 6- 24i`
Equating real and imaginary parts, we get
` 3x + 5y = -6`
`5x -3y = 24`
Sloving we get
`x = 3, y = -3`
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