Find the product of the given complex number and its conjugate.
$-7-i$

• A. $50$
• B. $14$
• C. $49$
• D. $1$

Answer: (A)

Verified step by step guidance

1. Identify the given complex number as \(-7 - i\) and its conjugate as \(-7 + i\). The conjugate of a complex number \(a + bi\) is \(a - bi\).
2. Set up the product of the complex number and its conjugate: \((-7 - i)(-7 + i)\).
3. Use the distributive property (FOIL method) to expand the product: \((-7)(-7) + (-7)(i) + (-i)(-7) + (-i)(i)\).
4. Simplify each term: \$49 - 7i + 7i - i^2\(. Notice that \)-7i\( and \)+7i$ cancel each other out.
5. Recall that \(i^2 = -1\), so replace \(-i^2\) with \(-(-1) = +1\). Then add the remaining terms: \$49 + 1$.