>>11120226

Squareroots are only poorly defined because information about absolute rotation, e.g. [math]e^{i3\pi}[/math] vs [math]e^{i\pi}[/math], is lost when converting to complex coordinates a+ib.

Likewise, multiplication of non-positive complex numbers is undefined. The only way we can derive meaningful information out of multiplication, without knowing the absolute rotation of the system, is by multiplying a number by its polar conjugate (the polar version of the complex conjugate, [math]ae^{i\theta}*be^{-i\theta}=ab e^{i0}[/math]. This is the polar equivalent of multiplying by zero, and acting surprised when multiplying (and dividing) by zero gives dumb answers.

In an ideal world, OP, I would call you an idiot. But this fundamental misunderstanding of polar coordinates is so deeply ingrained, I can only pity you, for you are but a mere product of your environment.