Answer: Choice B. 3√2
This is the same as writing 3sqrt(2) or [tex]3\sqrt{2}[/tex]
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Reason:
For any complex number of the form [tex]z = a+bi[/tex], the absolute value or magnitude of it is [tex]|z| = \sqrt{a^2+b^2}[/tex]
In this case, we have [tex]a = -4 \text{ and } b = -\sqrt{2}[/tex]
So,
[tex]|z| = \sqrt{a^2+b^2}\\\\|z| = \sqrt{(-4)^2+(-\sqrt{2})^2}\\\\|z| = \sqrt{16+2}\\\\|z| = \sqrt{18}\\\\|z| = \sqrt{9*2}\\\\|z| = \sqrt{9}*\sqrt{2}\\\\|z| = 3\sqrt{2}\\\\[/tex]
If we formed a segment with the endpoints [tex](0,0) \text{ and } (-4, -\sqrt{2} )[/tex], then that segment will have length of the value mentioned above.
Side note: This formula or concept is related to the pythagorean theorem.
