Question

What is the absolute value of the complex number -4 - square root of 2i

Answer 1

A) square root of 14

Answer 2

The absolute value of the complex number $z=a+bi$ is $|z|=\sqrt{a^2+b^2}.$

Consider the complex number $z=-4-\sqrt{2}i.$ For this complex number $a=-4$ and $b=-\sqrt{2}.$

Therefore, the absolute value of this complex number is

$|z|=\sqrt{(-4)^2+(-\sqrt{2})^2}=\sqrt{16+2}=\sqrt{18}=3\sqrt{2}.$

Answer: correct choice is B