9. Roots, Radicals, and Complex Numbers

Multiplying and Dividing Complex Numbers

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Multiple Choice

Find the product of the given complex number and its conjugate.
$- 7 - i$

$50$

$14$

$49$

$1$

Verified step by step guidance

Identify the given complex number as $-7 - i$ and its conjugate as $-7 + i$. The conjugate of a complex number $a + bi$ is $a - bi$.

Set up the product of the complex number and its conjugate: $(-7 - i)(-7 + i)$.

Use the distributive property (FOIL method) to expand the product: $(-7)(-7) + (-7)(i) + (-i)(-7) + (-i)(i)$.

Simplify each term: \$49 - 7i + 7i - i^2$. Notice that $-7i$ and $+7i$ cancel each other out.

Recall that $i^2 = -1$, so replace $-i^2$ with $-(-1) = +1$. Then add the remaining terms: \$49 + 1$.

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

Find the product of the given complex number and its conjugate.−7−i-7-i