The conjugate of a complex number is obtained by changing the sign of the imaginary part.

Given the complex number $3 - 6i$, its conjugate is:

$3 + 6i$

So, the conjugate of $3 - 6i$ is $3 + 6i$.

Would you like more details on this concept or have any questions?

Here are some related questions:

1. What is the conjugate of $2 + 4i$?
2. How do you find the magnitude of a complex number like $3 - 6i$?
3. What happens when you multiply a complex number by its conjugate?
4. How do you add and subtract complex numbers?
5. Can you explain how complex conjugates are used in dividing complex numbers?

Tip: Multiplying a complex number by its conjugate results in a real number, which is the sum of the squares of its real and imaginary parts.