text: # [SOLVED] Complex Polynomial Division
  
  • Jan 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.
  • Jan 25th 2010, 07:23 PM
  davismj
  Wait, nevermind. I see it now. Stupid mistake. Sorry.
  • Jan 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 $\frac{z^3 + i}{z - i} = \frac{(z - i)(z^2 + iz - 1)}{z - i}$
  
  $= z^2 + iz - 1$.