Does it matter where we put i?

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Discussion Overview

The discussion revolves around the placement of the imaginary unit i in mathematical expressions, particularly in relation to square roots. Participants explore whether the order of terms affects clarity and correctness in expressions involving complex numbers.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that it does not matter where i is placed as long as it is clear whether i is inside the square root or not.
  • Others argue that the order of terms does not affect the outcome due to the commutative and associative properties of complex numbers.
  • One participant mentions that it is better to position the imaginary number i in a way that it is not easily overlooked, recommending placing it at the beginning or end of an expression.
  • There is confusion regarding a specific expression that includes a division sign, leading to a discussion about its equivalence and clarity.
  • Participants express personal confusion about the notation used in various contexts, including references to how square roots are represented in different platforms.

Areas of Agreement / Disagreement

Participants express differing views on the clarity and implications of placing i in various positions within mathematical expressions. The discussion remains unresolved regarding the best practices for notation and clarity.

Contextual Notes

There are references to specific expressions and potential misunderstandings related to notation, particularly concerning the representation of square roots and division. The discussion highlights the importance of clarity in mathematical communication.

JR Sauerland
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In this problem, they solve for i, and at first, it looks like it will be i*2* square root of 3... Then he puts 2 sqrt of 3 times i. Can it also be 2i sqrt of 3?
 

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JR Sauerland said:
In this problem, they solve for i, and at first, it looks like it will be i*2* square root of 3... Then he puts 2 sqrt of 3 times i. Can it also be 2i sqrt of 3?
It doesn't matter where you put it as long as it's clear whether i is inside the square root or not. Also, it looks like 13 and not 3.

@Khang Click on the Physics Forums logo or the FORUMS tab. You will see a list of different forums. Select a forum and you will see a Post New Thread button on the top right of the page. Be sure to check the the Terms and Rules in the INFO tab before posting.
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Borg said:
It doesn't matter where you put it as long as it's clear whether i is inside the square root or not. Also, it looks like 13 and not 3.

@Khang Click on the Physics Forums logo or the FORUMS tab. You will see a list of different forums. Select a forum and you will see a Post New Thread button on the top right of the page. Be sure to check the the Terms and Rules in the INFO tab before posting.
View attachment 86688

Oops. I'm still a little sleepy. I'm saying that because someone told me I was wrong. I was seriously confused because I've seen professors write it as 2i sqrt of 13...
1.PNG
 
JR Sauerland said:
In this problem, they solve for i, and at first, it looks like it will be i*2* square root of 3... Then he puts 2 sqrt of 3 times i. Can it also be 2i sqrt of 3?
JR Souerland,
The order does not matter. Complex number satisfy the commutative property ##z_1 z_2 = z_2 z_1 ##, for any two complex numbers ## z_1## and ##z_2##. They also have the associative property ## z_1 (z_2 z_3) = (z_1 z_2) z_3##.

jason
 
JR Sauerland said:
In this problem, they solve for i, and at first, it looks like it will be i*2* square root of 3... Then he puts 2 sqrt of 3 times i. Can it also be 2i sqrt of 3?
Yes. But it's better to position the imaginary number i [/size] where it will not be easily overlooked, so in an expression write it first or else last, but don't hide it somewhere in the middle.
 
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JR Sauerland said:
Oops. I'm still a little sleepy. I'm saying that because someone told me I was wrong. I was seriously confused because I've seen professors write it as 2i sqrt of 13...
View attachment 86689
Well from your image, it looks like it says 2i divided by sqrt 13. That would be wrong.
 
JR Sauerland said:
Oops. I'm still a little sleepy. I'm saying that because someone told me I was wrong.
1.png
In that image, you show an expression that includes a division sign. That's presumably why you were told it would not be equivalent?
 
NascentOxygen said:
In that image, you show an expression that includes a division sign. That's presumably why you were told it would not be equivalent?

Yeah, I realized that after. I had gotten used to square root being expressed as /sqrt due to Mathway -_- and mylabsplus also uses /sqrt to create a square root sign lol. Woe is me.
 

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