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: multiply the first terms, outer terms, inner terms, and last terms.
4. Calculate each part: \((-7)(-7)\), \((-7)(i)\), \((-i)(-7)\), and \((-i)(i)\), keeping in mind that \(i^2 = -1\).
5. Combine like terms and simplify the expression to get the product, which will be a real number since the product of a complex number and its conjugate is always real.