Math Snap

STEP 1

Assumptions1. We have a complex number $-6-4i$.
. The conjugate of a complex number $a+bi$ is $a-bi$.

STEP 2

First, we need to find the conjugate of the given complex number. The conjugate of $-6-4i$ is $-6+4i$.

STEP 3

Now, we need to find the product of the complex number and its conjugate. The product of a complex number $a+bi$ and its conjugate $a-bi$ is $(a+bi)(a-bi)$.

STEP 4

Substitute $-6-4i$ and $-6+4i$ into the formula.
$(-6-4i)(-6+4i)$

STEP 5

Expand the product using the distributive property.
$(--4i)(-+4i) = (-)(-) + (-)(4i) - (4i)(-) - (4i)(4i)$

STEP 6

implify the expression.
$(-6-4i)(-6+4i) =36 -24i +24i -16i^2$

STEP 7

Remember that $i^2 = -1$. Substitute $-1$ for $i^2$ in the expression.
$(-6-4i)(-6+4i) =36 -24i +24i +16$

implify the expression.
$(-6-4i)(-6+4i) =52$
So, the product of $(-6-4i)$ and its conjugate is $52$.