What are the errors in this complex number equation?

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Discussion Overview

The discussion revolves around identifying errors in a complex number equation involving square roots and imaginary numbers. Participants analyze the steps taken in the equation and explore the implications of taking square roots in the context of complex numbers.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant presents a sequence of equalities leading to an incorrect conclusion of -4, questioning which step is erroneous.
  • Another participant suggests that the process is unnecessarily complicated and simplifies it to 4 = √16 = -4.
  • A different participant corrects the interpretation by emphasizing the absolute value, stating that the correct approach should involve taking the absolute value of the square roots, leading to 4 = |√16| = |-4|.
  • One participant acknowledges that the original assertion is incorrect but does not recall the specific mistake.
  • Another participant points out that the error lies in taking the wrong sign in front of the square root, noting that squaring and square rooting can introduce extraneous solutions.
  • A later reply expresses agreement with the previous correction, indicating a shared understanding of the issue.

Areas of Agreement / Disagreement

Participants generally agree that there is an error in the original equation, particularly regarding the sign of the square root. However, there are competing views on the steps taken and the nature of the errors involved.

Contextual Notes

Participants discuss the implications of taking square roots in the context of complex numbers, highlighting the potential for extraneous solutions without resolving the specific mathematical steps leading to the errors.

Who May Find This Useful

Individuals interested in complex numbers, mathematical reasoning, and the properties of square roots may find this discussion relevant.

expscv
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[tex]4 = \sqrt {4*4} = \sqrt {4*4*i^4} =\sqrt {i^2*4 *4*i^2}[/tex]

[tex]= i\sqrt{4}*i\sqrt{4} =2i*2i =-4[/tex]

this is wrong but which setp
=)
 
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You don't even have to go through that much work.

[tex]4 = \sqrt{16} = -4[/tex]

cookiemonster
 
That should be:
[tex]4 = |\sqrt {4*4}| = |\sqrt {4*4*i^4}| = |\sqrt {i^2*4 *4*i^2}|[/tex]
[tex]= |i\sqrt{4}*i\sqrt{4}| = |2i*2i| = |-4|[/tex]
Or just:
[tex]4 = |\sqrt{16}| = |-4|[/tex]
 
hehe oh? i was told that it sippose to be wrong
in somewhere that i forgot.
 
Well, it's wrong in that you're taking the wrong sign in front of the square root, but that's about it. Squares and square roots tend to generate extra solutions that are not necessarily correct. This is one such case.

cookiemonster
 
yep i agree, i remmber now haha
 

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