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
The text contains a mathematical question about simplifying a complex fraction and provides a step-by-step solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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
user
The text contains a mathematical question about simplifying a complex fraction and provides a step-by-step solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER