Mathematics

Mathematics

Problem

Let ω\omega be the complex number cos⁡2π3+isin⁡2π3\cos \frac{2\pi}{3} + i \sin \frac{2\pi}{3} , where i=−1i = \sqrt{-1} , then the number of distinct complex numbers zz satisfying ∣z+1ωω2ωz+ω21ω21z+ω∣=0\begin{vmatrix} z + 1 & \omega & \omega^2 \\ \omega & z + \omega^2 & 1 \\ \omega^2 & 1 & z + \omega \end{vmatrix} = 0 , is equal to a. 0 b. 1 c. 2 d. 3

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