Math Help - [SOLVED] Complex Polynomial Division

1. [SOLVED] Complex Polynomial Division

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

2. Wait, nevermind. I see it now. Stupid mistake. Sorry.

3. Originally Posted by davismj

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

$= z^2 + iz - 1$.