need help finding the coordinates of AB

Question

Find AB if the coordinate of A is -5 and the coordinate of B is 17. i have been out of school for over 20 years and have little to no memory of this process. i examined my daughter's book and there is absolutely NO reference to this material at all. please help me understand how to solve this equation?

Answer 1

You want $B-A$, the distance from $-5$ to $17$

Answer 2

The question is a little vague but I will answer what I think it means. I am presuming A is a vector with coordinates (0, -5) and B is a vector with coordinates (0,17); equivalently they are the complex numbers -5i and 17i. If you multiply them together you get (-5)(17)($i^2$) = 5x17.

For polar coordinates the angle (0, -5) makes with the x-axis is $-\pi/2$, so the polar coordinates of the endpoint are 5$e^{-i\pi/2}$. For B the angle of (0,17) is $\pi/2$ and the polar coordinates of the endpoint are 17$e^{i\pi/2}$.

To multiply these two numbers together you multiply the 5 and 17, and add the exponents on the e which come out to 0. So you get 5 x 17 x $e^0$ which is 5x17.

It's a little harder when the angle isn't $\pm 90^o$, but perhaps that is another subject.