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## Homework Statement

[tex] If arg(\frac{z-ω}{z-ω^2}) = 0, \ then\ prove \ that\ Re(z) = -1/2 [/tex]

## Homework Equations

ω and ω^2 are non-real cube roots of unity.

## The Attempt at a Solution

arg(z-ω) = arg(z-ω^2)

So, z-ω = k(z-w^2)

Beyond that, I'm not sure how to proceed. Using the rotation formula may also be required, but I'm not sure how to use it here.

Furthermore, I can sort of intuitively visualise the answer, but I'm not sure how to prove it analytically.

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