I recently came across the idea that two lines that are both parallel and perpendicular, exist in the complex plane. Obviously, I know this is probably silly, but I am interested to see what the flaw is in the equations below.
y = ix + 3
y = (-1/i)x + 2
When both slopes are multiplied by i/i, the slope of the first line remains the same at i but the second equation:
-1/i * i/i = -i/i^2
= -i/-1
= i
New slope: y = ix + 2
So this is proof that the lines are perpendicular and parallel. However, I know this is very flawed in some way, I believe it is something to do with a/a is always 1. I am interested to hear your thoughts...