Perform the indicated operation. Express your answer in standard form.
$open paren 3 plus 8 i close paren squared$

$-55+48i$

$9+64i$

$24i$

$9+24i$

Verified step by step guidance

Recognize that the problem requires squaring the complex number $3 + 8i$. This means calculating $(3 + 8i)^2$.

Use the formula for squaring a binomial: $(a + b)^2 = a^2 + 2ab + b^2$. Here, $a = 3$ and $b = 8i$.

Calculate each term separately: $a^2 = 3^2$, $2ab = 2 \times 3 \times 8i$, and $b^2 = (8i)^2$.

Remember that $i^2 = -1$, so when calculating $b^2 = (8i)^2$, rewrite it as $8^2 \times i^2 = 64 \times (-1)$.

Combine all the terms: add the real parts together and the imaginary parts together to express the result in standard form $x + yi$.

Master Multiplying Complex Numbers with a bite sized video explanation from Patrick Ford

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