JEE Main 2017Session, Shift 1MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002Let ω\omegaω be a complex number such that 2ω\omegaω + 1 = z where z = −3\sqrt {-3}−3. If ∣1111−ω2−1ω21ω2ω7∣=3k\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^7}} \cr } } \right| = 3k1111−ω2−1ω21ω2ω7=3k, then k is equal to :AOption A. zBOption B. -1COption C. 1DOption D. -zCheckSkip · show solution
