Problem involving complex numbers

[ubergewehr273]

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.

 

[Dick]

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?

 

[ubergewehr273]

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.

 

[Dick]

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?

 

[ubergewehr273]

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

 

[Dick]

Solution set includes (0,0,0) , (1,2,2), (2,4,4) and so on. This then gives a straight line. Thanks

Correct! You're very welcome.