1. Equations & Inequalities

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, which is $-7 - i$.

Find the conjugate of the complex number. The conjugate of $-7 - i$ is $-7 + i$.

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

Apply the formula for multiplying two binomials: $(a - b)(a + b) = a^2 - b^2$. Here, $a = -7$ and $b = i$.

Calculate $(-7)^2 - (i)^2$. Remember that $i^2 = -1$, so the expression becomes $49 - (-1)$.

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