You find an old map revealing a treasure hidden on a small island. The treasure was buried in the following way: the island has one tree and two rocks, one small one and one large one.
Walk from the tree to the small rock, turn 90 to the left and walk the same distance in that direction. Mark the point where you end up by A. Next, do the same for the big rock, but here turn 90 to the right. This way you end up at a point that is marked B. The treasure
is hidden halfway the line AB. You go to the island to find out that the tree no longer exists. How are you going to find the treasure?
For the first question, I can't really think of any relevant equations. The question is part of a course in complex analysis, so either using the vector representation of complex numbers, a + ib, or the polar coordinates, rei[itex]\theta[/itex] are bound to be in there somewhere, but how I don't see straight away.
For the second question, again from the complex analysis course, the most important formula that I can think of is the triangle inequality, |z1+z2|[itex]\leq[/itex]|z1|+|z2|
The Attempt at a Solution
Alright, the first question has me most puzzled. After drawing a few random situations, it seems as if the distance from rock one to the middle of AB is the same length as the distance of rock 2 to that same middle. This is all from just drawing mind you, so in no way proven. It also seems as if you walk to the middle of the two rocks and turn 90 degrees, you could dig a trench either down or up, until you find the treasure. Doesn't sound like a solid plan, either. Apart from this I don't really know where to begin. I've also had a lot of trouble approaching this issue not from a geometric side but from a point where I utilize complex functions instead. Could anyone give me a hint on where to start?
The second question I have gotten a bit further, but I somehow feel like either I did something wrong (plausible) or the equality sign in the question is the wrong way around (less plausible, but still possible).
Here's what I did:
I apologize for the images instead of latex, I should and will learn how to use it some time soon.