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Hi.

If you have seen the above image which shows a parabola then you can also see that there is a colored portion of the parabola that have solution in "another dimension" - the "another dimension" can give me new numbers to form a solution of a function like f(x) = x

^{2}+ 1.

1. Is this "another dimension" the third dimension 'Z' that I usually use to describe a three dimensional objects? I ask this question because the above video resource says that the graph shown in the video is in "full two dimensional form". Please seek the video to 1:39 where he says "full two dimensional form".

2. If the parabola drawn is not in three dimensions then what is the new dimension that the person referring to in the video called?

3. If I say that there is a complex number like 3 + 4i then is the real part of this complex number on the x-axis and the imaginary part of the complex number on this new dimension that the person pulls out with his hand from x-axis (at 1:40 seconds into the video)?

My thought:

According to me there are three dimensions: x, y, and the dimension that the person in the video creates with his hand.

4. In the complex number 3 + 4i where does 3 lie and where does 4 lie if I have these three dimensions?

5. Why does the parabola goes into the new dimension?

6. Why does the parabola looks the way it does in the video when I draw it with the new dimension?

Thanks!

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