Is there a known name for the commutation property in the complex absolute value formula? The supposed property can be resumed as follows:
The absolute value of a complex number remain unaltered when real and imaginary parts of complex number commute, $e.i$:
$|a + ib| = |b + ia| = a^2 + b^2$
may this be related to the fact that the absolute value for the imaginary unit $i$ and its mapping $i^*$ need to have the same absolute value?
$|i| = |i^*| = 1$?