Perform the indicated operation. Express your answer in standard form.
${(3+8i)}^2$

• A. $-55+48i$
• B. $9+64i$
• C. $24i$
• D. $9+24i$

Answer: (A)

Verified step by step guidance

1. Recognize that the problem asks you to square the complex number \(\left(3+8i\right)^2\), which means multiplying \$3+8i\( by itself: \)(3+8i)(3+8i)$.
2. Use the distributive property (FOIL method) to expand the product: multiply the first terms, outer terms, inner terms, and last terms: \$3 \times 3\(, \)3 \times 8i\(, \)8i \times 3\(, and \)8i \times 8i$.
3. Calculate each part separately: \$3 \times 3 = 9\(, \)3 \times 8i = 24i\(, \)8i \times 3 = 24i\(, and \)8i \times 8i = 64i^2$.
4. Combine the like terms: add the real parts \$9\( and \)64i^2\(, and add the imaginary parts \)24i + 24i$.
5. Remember that \(i^2 = -1\), so replace \$64i^2\( with \)64 \times (-1)\(, then simplify the real part and write the final expression in standard form \)a + bi$.