jee-advanced 2010 Q53

jee-advanced · India · paper1 Matrices Determinant and Rank Computation

Let $\omega$ be the complex number $\cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 }$. Then the number of distinct complex numbers $z$ satisfying $\left| \begin{array} { c c c } z + 1 & \omega & \omega ^ { 2 } \\ \omega & z + \omega ^ { 2 } & 1 \\ \omega ^ { 2 } & 1 & z + \omega \end{array} \right| = 0$ is equal to

Let $\omega$ be the complex number $\cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 }$. Then the number of distinct complex numbers $z$ satisfying $\left| \begin{array} { c c c } z + 1 & \omega & \omega ^ { 2 } \\ \omega & z + \omega ^ { 2 } & 1 \\ \omega ^ { 2 } & 1 & z + \omega \end{array} \right| = 0$ is equal to

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