Question

multiplying a complex number by a scalar
drag the point a to the location indicated in each scenario to complete each statement.

1. if a is in quadrant i and is multiplied by a negative scalar, c, then ca is in
2. if a is in quadrant ii and is multiplied by a positive scalar, c, then ca is in
3. if a is in quadrant ii and is multiplied by a negative scalar, c, then ca is in
4. if a is in quadrant iii and is multiplied by a negative scalar, c, then ca is in

Explanation:

1. A negative scalar flips the complex number's direction across the origin, moving a Quadrant I point to the opposite quadrant.
2. A positive scalar scales the number without changing direction, keeping a Quadrant II point in the same quadrant.
3. A negative scalar flips a Quadrant II point across the origin to the opposite quadrant.
4. A negative scalar flips a Quadrant III point across the origin to the opposite quadrant.

Answer:

1. Quadrant III
2. Quadrant II
3. Quadrant IV
4. Quadrant I