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

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 1: Find the conjugate of \( -6 - 24i \)

The conjugate of a complex number \( a + bi \) is \( a - bi \). Therefore, the conjugate of \( -6 - 24i \) is:
\[ -6 + 24i \]
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