Final answer:
The absolute value of the complex number -4 - square root of -2i is 2sqrt(6).
Step-by-step explanation:
The absolute value of a complex number is the distance between the complex number and the origin on the complex plane. In this case, the complex number is -4 - square root of -2i. To find the absolute value, we calculate the magnitude of the complex number using the Pythagorean theorem.
The magnitude is given by the formula |z| = sqrt(a^2 + b^2), where a and b are the real and imaginary parts of the complex number, respectively.
By substituting the values a = -4 and b = -sqrt(-2i) into the formula, we have |z| = sqrt((-4)^2 + (-sqrt(-2i))^2)).
Since the square root of -2i can be simplified as 2sqrt(2), we have |z| = sqrt((-4)^2 + (-2sqrt(2))^2) = sqrt(16 + 8) = sqrt(24) = 2sqrt(6).