: Here's a case where I've left out what I think are obvious steps, and : this person disagrees. Some may think it unnecessary for me to add : them, others may not.
: Here are the missing steps:
: Starting from (x+sqrt(-1)y)(x-sqrt(-1)y) = x^2 + y^2 = 0,
: (x+sqrt(-1)y)(x-sqrt(-1)= 0, so
: x + sqrt(-1)y = 0 or x -sqrt(-1)y = 0, so
: x = -sqrt(1)y or x = sqrt(-1)y.
: Some, for reasons I'd like them to explain, have complained that I : don't know that x + sqrt(-1)y = 0 or x -sqrt(-1)y = 0, if
: (x+sqrt(-1)y)(x-sqrt(-1)= 0.
: (Sort of like if AB = 0, A or B = 0. These people are saying that must : be proven, and that it is a "gap" in my proof that I don't do so.)
: If so, I'd like them to say that is their position here and we can see : if we can't work that one out.
Yes, that is my position. I would like an explanation of why it is true that if AB = 0, then A = 0 or B = 0. I grant that this statement is true when A and B are integers. However, I would like you to verify it when A and B are funny things like x + sqrt(-1)y and x - sqrt(-1)y (x, y integers).