[SOLVED] Complex Polynomial Division

**davismj** · January 25th 2010, 06:21 PM

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

**davismj** · January 25th 2010, 06:23 PM

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

**Prove It** · January 25th 2010, 07:09 PM

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

$= z^2 + iz - 1$ .

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