1. If the complex numbers $a, b, c$ are distinct, and the points they correspond to are $A, B, C, \omega=-\frac{1}{2}+\frac{\sqrt{3}}{2} \mathrm{i}$, and $a+\omega b+$ $\omega^{2} c=0$, then $\triangle A B C$ is
A. a right triangle
B. an obtuse triangle
C. an equilateral triangle
D. an isosceles right triangle
1. C $(a-c)+(b-c) \omega=0, a-c=\left(\cos 120^{\circ}+\operatorname{isin} 120^{\circ}\right)(c-b)$

1. C $(a-c)+(b-c) \omega=0, a-c=\left(\cos 120^{\circ}+\operatorname{isin} 120^{\circ}\right)(c-b)$

The above text is already in a mathematical format and does not contain any specific context that requires translation. However, if you meant to translate the surrounding text or provide a context, please provide more details. If the goal is to ensure the mathematical notation is clear in English, the notation itself is universally understood. Here is the text with the function name adjusted to the more common English notation:

1. C $(a-c)+(b-c) \omega=0, a-c=\left(\cos 120^{\circ}+i \sin 120^{\circ}\right)(c-b)$