Question 540721
If the argument of some complex number is 0, then the number must be a positive real number. Also, the numerator (z - omega) can be set to zero. We have

*[tex \LARGE \omega = -\frac{1}{2} + \frac{\sqrt{3}}{2}i \Rightarrow Re(\omega) = -\frac{1}{2}]


Since we want *[tex \LARGE Re(z - \omega) = 0] we set *[tex \LARGE Re(z) = \frac{1}{2}].