# Physical interpretation of complex numbers, part 2

I walk in the x direction, if I walk twice as fast, 2x, if I walk backwards, -x. What about ix? If I say that I walk an imaginary distance ix then this means in physics and maths that I walk perpendicular to the direction of x (there must be a new dimension).

If I scale an object by 2 in it's x dimension then it doubles in size, if I scale an object by -1 then I invert it. What happens when I scale an object by i? Then I change it's size in the direction perpendicular to x.

It appears to me that imaginary numbers are used to describe things happening in the dimensions that are orthogonal to the dimension being considered. It could be error away from a line, or another effect like magnetism acting perpendicular to the observed effect, it is about the actions perpendicular to the dimension being considered?

Is this a correct way to understand it?

If there are many perpendicular dimensions can they all be described by one single complex dimension? Do we transfer the information from many orthogonal dimensions into one complex dimension for ease of seeing how all the other dimensions in the system interact with the dimension we are studying?

• Please keep in mind that thinking about 'doubling in size' and such can be misleading since there is no ordering on complex numbers. – Ezze Nov 6 '19 at 12:43
• Ezze: Agreed, was writing for simplicity, the concept that using imaginary numbers is talking about dimensions perpendicular to the one being considered was the important idea I was trying to convey. Would you agree with this statement? – OzOz Nov 6 '19 at 12:50
• I do not fully understand what do you mean by perpendicular dimension. Is 'mass' perpendicular to 'frequency', for example? – Ezze Nov 6 '19 at 12:54
• I think you mean to say "if you scale by i, you rotate it 90 degrees". That's correct. – Abhimanyu Pallavi Sudhir Nov 6 '19 at 13:02
• Abhimanyu: Is that a correct description of the situation? It's not really about rotation, it's about things happening in a perpendicular dimension. If there are only 2 dimensions involved then you are correct, but with 3 dimensions, x, y, z, when you study the x dimension the y and z are complex, x + i(y+z) but if you study the y then y + I(x+z), which is not really a rotation by 90 degrees? It seems that the textbooks simplify it to the 2 dimension case where it is a 90 rotation? – OzOz Nov 6 '19 at 13:06