9. Roots, Radicals, and Complex Numbers

Multiplying and Dividing Complex Numbers

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

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