Question

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

Answer 1

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

Answer 2

Answer: (c)

The vector in the graph (c) has a magnitude of about

$|z|=\sqrt{(-5)^2+(-4)^2}=\sqrt{41}\approx6.40$

and the angle slightly less than 45 degrees from the x-axis as can be judged from the fact that it crosses the first box just below the point (-2,-2). This is the main distinction between (c) and (a) which is also similar in magnitude, however has an angle that is just larger than 45 degrees.