Let for some real numbers and , a = - i . If the system of equations 4ix + (1 + i)y = 0 and 8( (2 /3) + i (2 /3))x + āy = 0 has more than one solution, then / is equal to

JEE Main 2022 Mathematics question

Let for some real numbers and , . If the system of equations 4ix + (1 + i)y = 0 and + āy = 0 has more than one solution, then is equal to

(1)−2 +
(2)Correct
(3)
(4)−2 −

Answer: (2)

Solution

A homogeneous system of two equations has more than one solution when the determinant of its coefficients vanishes: 4i·ā − . So ā = 2(1 + i)(−1/2 + + i)(−1 +

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Question ID VK-034508