Solving Polynomials over C

Noir

I know this isn't in the right format, but I figured I'd get a better answer here than anywhere else. In my last exam, there was a question asking to prove (a + bi - except there were values for a and b, but i forgot them) was a solution to a polynomial of the 3rd degree.

Said polynomial was complex. I sub'd it in and got 0, so it worked. Here's the catch. To find the other two solutions, I subbed -1 in for i so the equation wasn't complex. I have no idea why I did it, i just remember it working. Lo and behold I got it right, the cubic equation I got had the same solutions as the quadratic you would get if you found used the long division method. I wasn't thinking and didn't want to deal with the i's.

I want to know, does the above methord work? Subbing in -1 for i and then solving? If it does I just went from a B to an A and I'm happy. I tried looking on the internet, but couldn't find anything.

Cheers,

James.

HallsofIvy

Unfortunately, I have no idea what you are saying. Do you mean that the coefficients of the polynomial themselves were complex numbers? It would help a lot if you were to show what polynomial you are talking about. In general replacing "i" with "-1" will not give you anything worhwhile ("i" and "-1" are NOT equal and one CANNOT replace the other) so it sounds like you were just lucky in this particular example.

Noir

Sorry for any confusion. Much like this equation right here;
z^4 + 3iz^3 - (4 + i)z^2 - 3iz + 3 + i = 0
I think your right; I was just lucky my dodgy maths worked! I don't see how replacing i with -1 would, or even could work now...