If I have two axes A (apples) and B (bananas), and I plot the point
where I have 3 apples and 4 bananas, then I would say I have 7 pieces
of fruit. However, Pythagoras would say I have 5 pieces of fruit
sqrt(3^2+4^2). Who is right, me or Pythagoras? :)
I came up with the axes of apples and bananas, because I don't
understand why two completely independent variables still have
something to do with each other through the pythagorean theorem.
The question came up as I was thinking about complex numbers. I
understand that the operation of "multiplying by i" is the same as
rotating 90 degrees anticlockwise. But I still don't understand what
happens with my apples if I multiply 3 apples by i. Do my apples
suddenly become bananas?
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