Question

Represent the product of A and B geometrically given that point A is located at (2, 45°) and B is located at (4, 45°). Give the coordinate of A • B in polar form.

Answer 1

Answer: (8,90°)

To get this answer, you multiply the r values together to get 2*4 = 8. At the same time, you add the theta angles to get 45° + 45° = 90°

The general rule is that if A = (r,theta) and B = (s,phi) then

A*B = (r*s,theta+phi)

where the point (s,phi) is a polar form point.

Answer 2

the coordinate of A • B is (8, 90°)

Explanation:

In polar form, points have two coordinates: (module, angle)

Defining: C = A • B

module of C = module of A • module of B

angle of C = angle of A + angle of B

Data: A = (2, 45°) and B = (4, 45°). Then:

module of C = 2 • 4 = 8

angle of C = 45° + 45° = 90°