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

Options

A. ` x = -2, y=2`
B. ` x = -3, y=3`
C. ` x = 3, y=-3`
D. ` x = -4, y=1`

Explanation

To solve the problem, we need to find the real numbers \( x \) and \( y \) such that \( (x - iy)(3 + 5i) \) is the conjugate of \( -6 - 24i \).

### Step-by-step Solution:

1. **Understanding the Conjugate**:
We know that the conjugate of a complex number \( z = a + bi \) is \( \bar{z} = a - bi \). Therefore, the conjugate of \( -6 - 24i \) is:
\[
\bar{z} = -6 + 24i
...