# [SOLVED] Complex Polynomial Division

• January 25th 2010, 07:21 PM
davismj
[SOLVED] Complex Polynomial Division
http://i49.tinypic.com/2m7hnro.png

However, this is wrong. It should be $z^2+zi-1$. I'm not sure how one would arrive here, however.
• January 25th 2010, 07:23 PM
davismj
Wait, nevermind. I see it now. Stupid mistake. Sorry.
• January 25th 2010, 08:09 PM
Prove It
Quote:

Originally Posted by davismj
http://i49.tinypic.com/2m7hnro.png

However, this is wrong. It should be $z^2+zi-1$. I'm not sure how one would arrive here, however.

Try using the Difference of Two Cubes Rule:

$z^3 + i = z^3 - (-i)$

$= z^3 - i^3$

$= (z - i)(z^2 + iz + i^2)$

$= (z - i)(z^2 + iz - 1)$.

So $\frac{z^3 + i}{z - i} = \frac{(z - i)(z^2 + iz - 1)}{z - i}$

$= z^2 + iz - 1$.