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, which is \(-7 - i\).
2. Find the conjugate of the complex number. The conjugate of \(-7 - i\) is \(-7 + i\).
3. Set up the expression for the product of the complex number and its conjugate: \((-7 - i)(-7 + i)\).
4. Apply the formula for multiplying two binomials: \((a - b)(a + b) = a^2 - b^2\). Here, \(a = -7\) and \(b = i\).
5. Calculate \((-7)^2 - (i)^2\). Remember that \(i^2 = -1\), so the expression becomes \(49 - (-1)\).