Question about Complex Numbers: Gauss Plane
Subject Mathematics
Mathematics
Source Originais Teachy
Originais Teachy
Topic Complex Numbers: Gauss Plane
Complex Numbers: Gauss Plane
Difficulty Medium
Medium
(Originais Teachy 2023) - Question Medium of Mathematics
In an imaginary city, each point on the map is represented by a complex number in the Gauss Plane. The city hall is located at the coordinate point z = 3 + 4i and the nearest hospital is at the point w = 1 - 2i. The mayor of the city, who was at the city hall, needs to go to the hospital. Considering that each unit on the map corresponds to 1 km in the city, what is the minimum distance the mayor needs to travel to reach the hospital? Additionally, in which quadrant of the Gauss Plane is the hospital located?a.
The minimum distance the mayor needs to travel to reach the hospital is 4√10 km and the hospital is located in the fourth quadrant of the Gauss Plane.
b.
The minimum distance the mayor needs to travel to reach the hospital is 2√10 km and the hospital is located in the second quadrant of the Gauss Plane.
c.
The minimum distance the mayor needs to travel to reach the hospital is 2√10 km and the hospital is located in the first quadrant of the Gauss Plane.
d.
The minimum distance the mayor needs to travel to reach the hospital is 2√10 km and the hospital is located in the third quadrant of the Gauss Plane.
e.
The minimum distance the mayor needs to travel to reach the hospital is 2√10 km and the hospital is located in the fourth quadrant of the Gauss Plane.
Answer sheet:
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