So it seems to be common consensus that the absolute value of a complex number is (a^2 b^2)^(1/2), but is this really true?

I understand that we use a two-dimensional graph to represent complex numbers, with the vertical axis generally being the imaginary component, and the horizontal axis being the real component, but to me it seems that this is just a simplified version of a more abstract reality.

If we consider the imaginary unit to be the √-1, then the Pythagorean Theorem shouldn't be able to work on the complex grid, as that would imply that √-1 is equal to 1, when it obviously isn't.

For example, if we take the number 3 3i, it's considered to havee an absolute value of √18, but it seems to me like its absolute value should just be 3 3i, as imaginary and real units are not interchangeable.

Does anyone have a better way to explain this? Please let me know what I'm missing.

Thank you.

EDIT: I'm realizing that the way I've worded the question above can be misleading. I'm not confused about the distance between points via the Cartesian grid. I'm more confused about why we consider the imaginary number to be within its own spatial dimension. I thought that the Cartesian grid was just a representation of a more abstract number line.

EDIT #2: I've got it now. Thank you all for explaining it to me.