Why is \( (1 + \sqrt{-5}) \times (1 - \sqrt{-5}) \) Equal to 6?

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Discussion Overview

The discussion revolves around the expression \( (1 + \sqrt{-5}) \times (1 - \sqrt{-5}) \) and why it equals 6. Participants explore the calculation and the implications of using imaginary numbers, with a focus on the mathematical reasoning behind the result.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant questions the equality of the expression and seeks clarification.
  • Another participant suggests expanding the expression as a method to understand the calculation.
  • A participant expresses unfamiliarity with imaginary numbers, indicating a gap in understanding.
  • Another response proposes treating \( \sqrt{-5} \) as an unknown number to simplify the problem without delving into imaginary numbers.
  • A correction is made regarding a typographical error in the original question, clarifying the expression being discussed.
  • One participant explains that the expression represents a difference of squares, leading to the conclusion that it equals \( 1 - (-5) \).
  • A later comment indicates a perceived lack of effort from the original poster, leading to a closure of the thread.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding imaginary numbers and the calculation process. There is no consensus on the approach to solving the problem, and the discussion remains unresolved due to the closure of the thread.

Contextual Notes

Some participants rely on different levels of familiarity with imaginary numbers, which may affect their understanding of the problem. The discussion also highlights a potential misunderstanding of mathematical notation and expression expansion.

harrylentil
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Why is (1 + sqrt(-5) x (1 – sqrt(-5)) equal to 6?
 
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Did you expand the expression?

Do you know about imaginary numbers? You don't have to to calculate the expression, but it helps understanding what is going on.
 
I don't know how to work with imaginary numbers.
 
Then just imagine that sqrt(-5) is some number that you don't know. You don't have to use imaginary numbers to solve the problem.
 
Typo in my original question - a right bracket is missing. It should be,
Why is (1 + sqrt(-5)) x (1 – sqrt(-5)) equal to 6?

Anyone?
 
mfb said:
Did you expand the expression?
 
You just have a difference of squares: (a+b)(a-b) = a^2-b^2 which, in your case means: (1 + sqrt(-5)) (1 – sqrt(-5)) = 1 - (-5)
 
Since Juan has shown the OP how to do this, and the OP keeps refusing to show any effort, this thread is now closed (after some cleanup)
 

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