(6-i)(6+i)

Jasonbradley

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Jun 16, 2024

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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:

1. Identify 'a' and 'b':

   • a = 6
   • b = i

2. Substitute into the pattern:

   • (6 - i)(6 + i) = 6² - i²

3. 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.