JEE Main 2024 Mathematics question

MathematicsComplex NumbersJEE Main 2024

If z is a complex number, then the number of common roots of the equations z¹⁹⁸⁵ + z¹⁰⁰ + 1 = 0 and z³ + 2z² + 2z + 1 = 0, is equal to

Answer: (A)

Solution

z³ + 2z² + 2z + 1 = (z + 1)(z² + z + 1) = 0 gives z = −1, ω, ω². z = −1 does not satisfy the first equation, since (−1)¹⁹⁸⁵ + (−1)¹⁰⁰ + 1 = 1. For z =

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Question ID VK-016993