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 as \$4 - 5i\( and its conjugate as \)4 + 5i\(. The conjugate of a complex number \)a + bi\( is \)a - bi$.
2. Set up the product of the complex number and its conjugate: \((4 - 5i)(4 + 5i)\).
3. Use the distributive property (FOIL method) to expand the product: multiply the first terms, outer terms, inner terms, and last terms.
4. Recall that \(i^2 = -1\), so simplify the terms involving \(i^2\) accordingly.
5. Combine like terms (real parts and imaginary parts) to write the product as a real number.