Question

what is the absolute value of the complex number $-4 - sqrt{2}i$?
$circ$ $sqrt{14}$
$circ$ $3sqrt{2}$
$circ$ $14$
$circ$ $18$

Explanation:

Step1: Recall complex absolute value formula

For complex number $a+bi$, $|a+bi|=\sqrt{a^2+b^2}$

Step2: Identify $a$ and $b$

Here, $a=-4$, $b=-\sqrt{2}$

Step3: Substitute into formula

$| -4-\sqrt{2}i |=\sqrt{(-4)^2+(-\sqrt{2})^2}$

Step4: Calculate squared terms

$(-4)^2=16$, $(-\sqrt{2})^2=2$

Step5: Sum and simplify root

$\sqrt{16+2}=\sqrt{18}=3\sqrt{2}$

Answer:

$3\sqrt{2}$ (corresponding to the second option)