How can I express SQRT(27) in terms of i and cancel out the i?

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Homework Help Overview

The discussion revolves around expressing SQRT(27) in terms of the imaginary unit i and simplifying the expression. Participants are exploring the nature of square roots and their potential complex representations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to express SQRT(27) using complex numbers and questioning the validity of their approaches. Some express confusion about the relationship between square roots and imaginary numbers, while others reflect on their understanding of sine and cosine functions in relation to the problem.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants are questioning their previous reasoning and assumptions, while others are trying to clarify the mathematical principles involved. There is no explicit consensus on how to proceed, but several participants are actively engaging with the problem.

Contextual Notes

Some participants express uncertainty about the definitions and properties of square roots, particularly in relation to complex numbers. There are indications of confusion regarding the application of trigonometric functions and their values.

GreenPrint
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Homework Statement



I was trying to do this problem and noticed that I should be able to express SQRT(27) in terms of i and cancle out the i making it more simple I can't seem to remember how to do this thanks

[IMG=http://img294.imageshack.us/img294/5396/captureow.jpg][/PLAIN]

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Homework Equations





The Attempt at a Solution

 
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here you go sorry about that

[PLAIN]http://img294.imageshack.us/img294/5396/captureow.jpg

i need to solve for x don't remeber how to do this
 
Last edited by a moderator:
If you're looking for the solutions to x2 - 27 = 0, they are the real numbers [itex]x = 3\sqrt{3}[/itex] and [itex]x = -3\sqrt{3}[/itex]. Otherwise, I have no idea what you're trying to do.
 
I think i may have just proved
SQRT(27) = -27
did something wrong but I did it step by step let me look at this :(
 
I'll show you in a moment I think i may have just proved SQRT(27) = -27
I don't think I have done anything wrong this is really weird let me type it up... hope I'll find something wrong because if i don't... :O
 
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Last edited by a moderator:
but you that form is better to use becasue then you can cancel out the pi and your left with i raised to some fraction much easier to evalute no? but you i guess i misse dup some where and did it wrong but it works
 
  • #10
well that sure is strange I never was taught that form of sin I just wen through the derrivation i guess of euelr's sine formula and screwed up somewhere but it's right

wounder why I have never encountered it before i think it would be much easier to use no
 
  • #11
I think I have messed up when I did SQRT(3) as an example sorry
 
  • #12
Well see what I think I need to do is take my sine equation and set it equal to sqrt(37) sine can take on any value those who say it's llimited betweeen 1 and negative one are liers... and then solve so when solved earlier I think I was doing it right I thinkI just need to start over
 
  • #13
well i guess in theory I should have just done this

http://img706.imageshack.us/img706/4708/capturefeb.jpg

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and solved for x since sine can take on any value it wants then just do sin(x) would truly be the most simplifed huh?
I think that would be a better way to do it instead of setting it equal to sqrt(27) yes I know realize I forgot the initial 1/2 when I original atempted and set it eqaul to sqrt(27) so should i set it equal to sqrt(27) or just the whole darn thing
 
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  • #14
I take that back what I originally did wasn't wrong as that should be able to take on any number that it desires as well no and then I could cancel out the i if I had one in the denomenator, in post number seven I guess I just did something wrong...
 
  • #15
well i just had this great idea that I'm going to work out tommarow I am going to set cosine=sine
yes that's
cos(x)=sin(x)
or in common terms what angle does cosine and sine have the same value... none? Don't think so my friend I'm not buying it... I just woundering what will happen I am going to solve it...

sorry by the way i started out trying to do that problem then got into sine and this idea just poped into my head and was like well i should be able to solve that technically speaking...

well i just did it everything canceled out I wounder what that means oh crap maybe you guys were right there is none =(
 
  • #16
GreenPrint said:
I think i may have just proved
SQRT(27) = -27

This is ridiculous. If this were true, the 27 = (-27)2 would also be true. Obviously, it isn't.

sqrt(27) is not a complex number, so why are you even bothering to go down that path?

In its simplest form, sqrt(27) is 3sqrt(3).
 

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