- #1
DiracPool
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I'm trying to get straight some basic complex number fundamentals.
First we have z=x+iy. Ok, my question is what does the z in the equation represent? Does it represent a "point" on the complex plane? Does it represent a vector from the origin to where the x and iy values add? Does it represent the "length" of that resultant vector?
I'm guessing it doesn't represent the length of the vector, z, because I read that the length of that vector is the squared modulus of z^2=x^2+(iy)^2. I'm guessing that if we didn't take the modulus, we'd end up with an equation which gave us a length of z=√x^2-y^2. Why are we allowed just to take the modulus here and not worry about it? Just because it gives us a Pythagorean "real" looking length? It seems incorrect. It seems as though the length should be as the equation states, z=√x^2-y^2. What am I missing here?
But my main question is what does the z in the z=x+iy represent? And could you give me the equivalent on how that would look on just the ordinary "real" x-y plane.
I know this sounds elementary, but I just haven't been able to find a straightforward explanation anywhere.
First we have z=x+iy. Ok, my question is what does the z in the equation represent? Does it represent a "point" on the complex plane? Does it represent a vector from the origin to where the x and iy values add? Does it represent the "length" of that resultant vector?
I'm guessing it doesn't represent the length of the vector, z, because I read that the length of that vector is the squared modulus of z^2=x^2+(iy)^2. I'm guessing that if we didn't take the modulus, we'd end up with an equation which gave us a length of z=√x^2-y^2. Why are we allowed just to take the modulus here and not worry about it? Just because it gives us a Pythagorean "real" looking length? It seems incorrect. It seems as though the length should be as the equation states, z=√x^2-y^2. What am I missing here?
But my main question is what does the z in the z=x+iy represent? And could you give me the equivalent on how that would look on just the ordinary "real" x-y plane.
I know this sounds elementary, but I just haven't been able to find a straightforward explanation anywhere.