I have a question for whoever has an answer, but it requires a bit of context. When I saw the part of the question asking to find the maximum and minimum values of |z|, my first thought was to do something similar to what one does when solving an electrostatics problem. In electrostatics, we’re usually interested in finding the force a test charge feels due to a source charge somewhere else. So the relative separation between a source charge q and a test charge Q is important because of Coulomb’s law. This separation is calculated by subtracting the position vector of the source charge r from the position vector of the test charge R (so it’s (R-r)) and then taking the magnitude of the difference. In this problem, the source charge q would be at 2+i and Q would be somewhere on the circle. As we move the test point clockwise around the circle, the angle between the separation vector (R-r) and the position vector of the source charge r goes from 0 to 2π. The angles 0 and π coincide with the minimum and maximum values (respectively) we were looking for which are also the values where cosine is maximized and minimized. From this, I feel like there’s some trigonometry lurking in the background. Finally to my question: since the three vectors r, R, and (R-r) form a triangle and we have an angle of interest between the vectors (R-r) & r is this the law of cosines at work? By “at work” I mean we can infer the max and min values of |z| using the law of cosines through the angle between (R-r) and r. I know my setup is a bit of a mess so if something isn’t clear, I’m happy to clarify. For Eddie, the video was great!
Um, not a clue what he was on about but I'm just glued to this guy's enthusiasm. 👍
Eddie. These videos are very much appreciated. Thank-you. From a retired maths teacher.
I have a question for whoever has an answer, but it requires a bit of context.
When I saw the part of the question asking to find the maximum and minimum values of |z|, my first thought was to do something similar to what one does when solving an electrostatics problem. In electrostatics, we’re usually interested in finding the force a test charge feels due to a source charge somewhere else. So the relative separation between a source charge q and a test charge Q is important because of Coulomb’s law. This separation is calculated by subtracting the position vector of the source charge r from the position vector of the test charge R (so it’s (R-r)) and then taking the magnitude of the difference. In this problem, the source charge q would be at 2+i and Q would be somewhere on the circle. As we move the test point clockwise around the circle, the angle between the separation vector (R-r) and the position vector of the source charge r goes from 0 to 2π. The angles 0 and π coincide with the minimum and maximum values (respectively) we were looking for which are also the values where cosine is maximized and minimized. From this, I feel like there’s some trigonometry lurking in the background.
Finally to my question: since the three vectors r, R, and (R-r) form a triangle and we have an angle of interest between the vectors (R-r) & r is this the law of cosines at work? By “at work” I mean we can infer the max and min values of |z| using the law of cosines through the angle between (R-r) and r.
I know my setup is a bit of a mess so if something isn’t clear, I’m happy to clarify.
For Eddie, the video was great!
This was so well explained!
Love the video.
super clear. I don't recall, using that name for the technique but I do it in a similar way.
Thank you! I love having well explained examples, saludos de argentina!!
I find it easier to understand |x|≤a / |x|≥a by just drawing a number line and reasoning through it but the graph explanation is pretty nice
second
LOL from India 🇮🇳
henlo