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

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

Answer: (A)

Verified step by step guidance

1. Start by recognizing that you need to square the complex number (3 + 8i). This means you will multiply (3 + 8i) by itself.
2. Apply the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2. Here, a = 3 and b = 8i.
3. Calculate a^2: (3)^2 = 9.
4. Calculate 2ab: 2 * 3 * 8i = 48i.
5. Calculate b^2: (8i)^2 = 64i^2. Remember that i^2 = -1, so 64i^2 = 64 * (-1) = -64.