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 $\frac{z^3 + i}{z - i} = \frac{(z - i)(z^2 + iz - 1)}{z - i}$
  
  $= z^2 + iz - 1$.
explanation: The document is a forum post about a math problem involving complex polynomial division. The user initially asks for help with a specific polynomial division problem, stating that their result is incorrect and should be \(z^2 + zi - 1\). However, the user then realizes their mistake and apologizes for the post. Another user provides a detailed solution using the Difference of Two Cubes Rule.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # [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 $\frac{z^3 + i}{z - i} = \frac{(z - i)(z^2 + iz - 1)}{z - i}$
  
  $= z^2 + iz - 1$.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum post about a math problem involving complex polynomial division. The user initially asks for help with a specific polynomial division problem, stating that their result is incorrect and should be \(z^2 + zi - 1\). However, the user then realizes their mistake and apologizes for the post. Another user provides a detailed solution using the Difference of Two Cubes Rule.
  
  Label: question-and-answer