Question
How is the product of a complex number and a real number represented on the coordinate plane?
A)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar and a counterclockwise rotation of 90° of the complex number.
B)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a counterclockwise rotation of 90° of the complex number.
C)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar of the complex number.
D)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar and a clockwise rotation of 90° of the complex number.
A)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar and a counterclockwise rotation of 90° of the complex number.
B)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a counterclockwise rotation of 90° of the complex number.
C)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar of the complex number.
D)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar and a clockwise rotation of 90° of the complex number.
Answers
Reiny
multiplying a complex number by a scalar does not affect the angle in the Argand plane.
Thus no rotation is involved, it merely affects the magnitude.
e.g. 3 + 2i
tanØ = 2/3
3(3 + 2i) = 9 + 6i
tanØ = 6/9 = 2/3 , angle did not change
magnitude of 3 + 2i = √(9+4) = √13
magnitude of 9 + 6i = √(81+36) = √117 = √9*√13 = 3√13 <--- 3 times as long
Thus no rotation is involved, it merely affects the magnitude.
e.g. 3 + 2i
tanØ = 2/3
3(3 + 2i) = 9 + 6i
tanØ = 6/9 = 2/3 , angle did not change
magnitude of 3 + 2i = √(9+4) = √13
magnitude of 9 + 6i = √(81+36) = √117 = √9*√13 = 3√13 <--- 3 times as long