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: \(-7 - i\).
2. Write down the conjugate of the complex number by changing the sign of the imaginary part: the conjugate of \(-7 - i\) is \(-7 + i\).
3. Set up the product of the complex number and its conjugate: \((-7 - i)(-7 + i)\).
4. Use the difference of squares formula to multiply: \((a - b)(a + b) = a^2 - b^2\), where \(a = -7\) and \(b = i\).
5. Calculate \(a^2 - b^2\) as \((-7)^2 - (i)^2\), remembering that \(i^2 = -1\).