If the magnitude of vector z is ||z|| ≈ 6.40 and its angle of direction is approximately 38.66°, which graph represents vector -z?

graph C represents - z

z = (6.40, 38.66°) which is in the first quadrant

- z is in the opposite direction to z and in fourth quadrant.

Both graphs, however, are in the fourth quadrant

consider the magnitudes of both complex numbers to determine which graph is the correct one

Graph C has endpoint at (- 5, - 4 ), hence

magnitude = √((- 5)² + (- 4)²) = √(25 + 16) = √41 ≈ 6.4

Graph D has endpoints (- 3, - 6), hence

magnitude = √((- 3)² + (- 6)²) = √(9 + 36) = √45 ≈ 6.7

4

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this is a very good question

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