text: 1. ## simplify the equation
  
  I need to simplify (i^2+2i+1)/(-i^2+1) to the form #i where # is any coefficient.
  
  2. Originally Posted by hayter221
  I need to simplify (i^2+2i+1)/(-i^2+1) to the form #i where # is any coefficient.
  Remember that $\displaystyle i^2 = -1$
  
  So,
  
  $\displaystyle \frac{i^2 + 2i +1}{-i^2 + 1}$
  
  $\displaystyle = \frac{-1 + 2i + 1}{1 + 1}$
  
  $\displaystyle = \frac{2i}{2}$
  
  $\displaystyle = 1i$ or just i
explanation: The document contains a math question and a detailed answer to the question. The question asks how to simplify a given complex fraction to the form #i, and the answer provides step-by-step simplification.
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distilabel_metadata.role: system
distilabel_metadata.content: 1. ## simplify the equation
  
  I need to simplify (i^2+2i+1)/(-i^2+1) to the form #i where # is any coefficient.
  
  2. Originally Posted by hayter221
  I need to simplify (i^2+2i+1)/(-i^2+1) to the form #i where # is any coefficient.
  Remember that $\displaystyle i^2 = -1$
  
  So,
  
  $\displaystyle \frac{i^2 + 2i +1}{-i^2 + 1}$
  
  $\displaystyle = \frac{-1 + 2i + 1}{1 + 1}$
  
  $\displaystyle = \frac{2i}{2}$
  
  $\displaystyle = 1i$ or just i
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed answer to the question. The question asks how to simplify a given complex fraction to the form #i, and the answer provides step-by-step simplification.
  
  Label: question-and-answer