Question
Let $z_{1}, z_{2}, z_{3}$ be the vertices of an equilateral triangle. If $\frac{z_{1}-z_{2}}{z_{3}-z_{2}}=z$ then $1+z+z^{2}$ is equal to(a) 0(b) $2 \omega$(c) $\omega$(d) $-2 \omega^{2}$
Step 1
For an equilateral triangle, we can write $z_{1}-z_{2} = (z_{3}-z_{2})e^{i\pi/3}$, where $e^{i\pi/3}$ is the rotation operator for an angle of $\pi/3$. Show more…
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