To solve \((-7 - i)(-7 + i)\), we can apply the **difference of squares** formula:

\[
(a - b)(a + b) = a^2 - b^2
\]

In this case:
- \(a = -7\)
- \(b = i\)

Thus, the expression becomes:

\[
(-7 - i)(-7 + i) = (-7)^2 - (i)^2
\]

Now compute each part:
- \((-7)^2 = 49\)
- \(i^2 = -1\) (since \(i^2 = -1\))

Substituting back in:

\[
49 - (-1) = 49 + 1 = 50
\]

So, the result of \((-7 - i)(-7 + i)\) is \( \boxed{50} \).

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:
1. What is the general form of complex numbers?
2. How do you simplify the product of two complex conjugates?
3. Can you apply the difference of squares to non-complex numbers?
4. What is the significance of \(i^2 = -1\)?
5. How would you expand \((a - b)(a + b)\) for other values?

**Tip:** When multiplying complex conjugates, the result is always a real number.

Discover how to multiply the complex conjugates (-7 - i) and (-7 + i) using the difference of squares formula. This step-by-step guide explains key concepts from algebra and complex numbers, suitable for students in Grades 9-11.

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