Simplifying (6  i)(6 + i)
This expression involves multiplying two complex numbers together. We can simplify this using the difference of squares pattern:
 (a  b)(a + b) = a²  b²
Here's how we can apply this to our expression:

Identify 'a' and 'b':
 a = 6
 b = i

Substitute into the pattern:
 (6  i)(6 + i) = 6²  i²

Simplify:
 6²  i² = 36  (1) (Remember that i² = 1)
 36  (1) = 36 + 1 = 37
Therefore, (6  i)(6 + i) simplifies to 37.
This demonstrates that multiplying a complex number by its conjugate (the number with the opposite sign of the imaginary part) results in a real number.