A tricky question with complex numbers

  • #26
249
24
This seems to be the pair (3/7,4/7).
thanks i got it.
 
  • #27
249
24
That's not correct. But, as I said, you don't actually need to find the point.
so how we will do it without finding the point.
 
  • #28
PeroK
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so how we will do it without finding the point.
You're only asked for the sum of the distances. You don't need to calculate the point for that.
 
  • #29
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Yes, exactly, any point on the line segment between the two points in question. You can, of course, use the triangle inequality to prove that, if you wish.

Now, that leaves two more points to deal with.
I think I got it. Any point on the line passing by ##(0,1)## and ##(1,0)## minimizes the distance between them, it is also the same for the origin and ##(3,4)##, so ##z## that minimizes that equation should be the point of intersection of both lines.
 
  • #30
PeroK
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I think I got it. Any point on the line passing by ##(0,1)## and ##(1,0)## minimizes the distance between them, it is also the same for the origin and ##(3,4)##, so ##z## that minimizes that equation should be the point of intersection of both lines.

Yes. And you know the sum of the distances in both cases, so you don't even need to calculate the point - as long as geometrically you can see it exists.
 
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