The graph from which the position of the point A can determined following
the multiplication with a scalar is attached.
Responses:
- If A is in quadrant I and is multiplied by a negative scalar, c, then c·A is in quadrant III
- If A is in quadrant II and is multiplied by a positive scalar, c, then c·A is in quadrant II
- If A is in quadrant II and is multiplied by a negative scalar, c, then c·A is in quadrant IV
- If A is in quadrant III and is multiplied by a negative scalar, c, then c·A is in quadrant I
Methods by which the above responses are obtained
Background information;
The question relates to the coordinate system with the abscissa represent the real number and the ordinate representing the imaginary number.
Solution:
If A is in quadrant I; A = a + b·i
When multiplied by a negative scalar, c, we get;
c·A = c·a + c·b·i
Therefore;
c·a is negative
c·b is negative
- c·A = c·a + c·b·i is in the quadrant III (third quadrant)
If A is quadrant II, we have;
A = -a + b·i
When multiplied by a positive scalar c, we have;
c·A = c·(-a) + c·b·i = -c·a + c·b·i
-c·a is negative
c·b·i is positive
Therefore;
- c·A = -c·a + c·b·i is in quadrant II
Multiplying A by negative scalar if A is in quadrant II, we have;
c·A = -c·a + c·b·i
-c·a is positive
c·b·i is negative
Therefore;
c·A = -c·a + c·b·i is in quadrant IV
If A is in quadrant III, we have;
A = a + b·i
a is negative
b is negative
Multiplying A with a negative scalar c gives;
c·A = c·a + c·b·i
c·a is positive
c·b is positive
Therefore;
- c·A = c·a + c·b·i is in quadrant I
Learn more about real and imaginary numbers here;
https://brainly.com/question/5082885
https://brainly.com/question/13573157
