> it comes down to the definition of imaginary itself,
which is a number involving i. 0i is imaginary,

It is only a matter of definition because that is not my definition of imaginary. An element of the field of complex numbers? Absolutely.

An
element of the subgroup of imaginary numbers
**I** = {bi|b in **R**}? Again absolutely. But my definition of imaginary number is a complex number a + bi with a = 0 and b nonzero.

Wayne

Joe wrote...

"By any number of approaches (see Wikipedia, for example) I think we would see that zero is both real and imaginary, and that makes the statement false. If one disagrees with that, its because they like definitions that are crafted to avoid that conclusion,
much like politics."

I didn't search long, but the arguments for zero being both real and imaginary seem to involve complex numbers and the complex plane. For example, since the two axes of the complex plane intersect at 0 then 0 must be both real and imaginary. But the axes don't
intersect at 0, they intersect at (0,0). Likewise, the notion that 0i is 0 (in the context of this problem) is also troublesome. When you reduce 0i to 0, it is no longer imaginary or complex. Do you know of any approaches that avoid this dilemma? I guess it
comes down to the definition of imaginary itself, which is a number involving i. 0i is imaginary, but 0 (without the i) is not.

Bob