Find the product of the given complex number and its conjugate.
$4-5i$

• A. $16$
• B. $41$
• C. $25$
• D. $20$

Answer: (B)

Verified step by step guidance

1. Identify the given complex number, which is \$4 - 5i\(, where \)4\( is the real part and \)-5$ is the imaginary part.
2. Write down the conjugate of the complex number. The conjugate of \(a + bi\) is \(a - bi\), so the conjugate of \$4 - 5i\( is \)4 + 5i$.
3. Set up the product of the complex number and its conjugate: \((4 - 5i)(4 + 5i)\).
4. Use the distributive property (FOIL method) to multiply the two binomials: multiply the first terms, outer terms, inner terms, and last terms.
5. Simplify the expression by combining like terms and using the fact that \(i^2 = -1\) to rewrite the product in terms of real numbers only.