Question

What is the absolute value of the complex number -4-√2i?

A.√14
B.3√2
C.14
D.18
PLEASE HELP

Answer 1

Answer: Choice B. 3√2

This is the same as writing 3sqrt(2) or
`3√(2)`

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Reason:

For any complex number of the form
`z = a+bi`, the absolute value or magnitude of it is
`|z| = √(a^2+b^2)`

In this case, we have
`a = -4 \text{ and } b = -√(2)`

So,

`|z| = √(a^2+b^2)\\\\|z| = \sqrt{(-4)^2+(-√(2))^2}\\\\|z| = √(16+2)\\\\|z| = √(18)\\\\|z| = √(9*2)\\\\|z| = √(9)*√(2)\\\\|z| = 3√(2)\\\\`

If we formed a segment with the endpoints
`(0,0) \text{ and } (-4, -√(2) )`, then that segment will have length of the value mentioned above.

Side note: This formula or concept is related to the pythagorean theorem.