Problem involving complex numbers

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Homework Help Overview

The discussion revolves around a problem involving complex numbers and determinants, specifically focusing on the equation w^2 + w + 1 = 0, where w represents the cube root of unity. Participants are examining the conditions under which a determinant equals zero and the implications of that condition.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss expanding a determinant and the resulting equation. There are attempts to analyze the implications of the imaginary parts canceling when the determinant is zero. Questions arise regarding the geometric interpretation of the solution set based on relationships derived from comparing real and imaginary components.

Discussion Status

The discussion is active, with participants exploring various interpretations of the relationships between variables. Some guidance has been offered regarding the cancellation of imaginary parts, and there is an ongoing exploration of the geometric nature of the solution set.

Contextual Notes

Participants are working under the constraints of a homework problem, referring to a given image that is not included in the discussion. The nature of the problem suggests that assumptions about the relationships between variables are being questioned.

ubergewehr273
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Homework Statement


Refer given image.

Homework Equations


Expansion of determinant.
w^2+w+1=0 where w is cube root of 1.

The Attempt at a Solution


Expanding the determinant I got cw^2+bw+a-c=0. Well after that I have no idea how to proceed.
 

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ubergewehr273 said:

Homework Statement


Refer given image.

Homework Equations


Expansion of determinant.
w^2+w+1=0 where w is cube root of 1.

The Attempt at a Solution


Expanding the determinant I got cw^2+bw+a-c=0. Well after that I have no idea how to proceed.

If the determinant is going to be zero then the imaginary parts must cancel. What does that tell you?
 
Dick said:
If the determinant is going to be zero then the imaginary parts must cancel. What does that tell you?
I compared the real and imaginary parts separately and ended up with the relation a=2b=2c.
 
ubergewehr273 said:
I compared the real and imaginary parts separately and ended up with the relation a=2b=2c.

Ok, so what does that tell you about the geometry of the solution set?
 
Dick said:
Ok, so what does that tell you about the geometry of the solution set?
Solution set includes (0,0,0) , (1,2,2), (2,4,4) and so on. This then gives a straight line. Thanks :bow:
 
ubergewehr273 said:
Solution set includes (0,0,0) , (1,2,2), (2,4,4) and so on. This then gives a straight line. Thanks :bow:

Correct! You're very welcome.
 

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