Whoops.
So, the complex numbers root(1/2) - root(1/2)j, and, - root(1/2) + root(1/2)j are valid roots of j.
Looks like I typed that bit wrong.
root(j) = root(-1/2) - root(-1/2)j, or, root(j) = - root(-1/2) + root(-1/2)j was right.
My google-fu is good enough for this, however.
Now I come to think of it, you could probably cancel (root(-1/2) - root(-1/2)j) to one of the original roots, and likewise with the other one...
root(-1/2) - root(-1/2)j = root(1/2)j + root(1/2)
- root(-1/2) + root(-1/2)j = - root(1/2)j - root(1/2)
which are the original roots. Oh well, ignore me then.
Though, I still don't understand why you can't make a or b complex or imaginary; so long as a + bj is complex or imaginary, it shouldn't matter, should it? |
