JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

Given the equation z^2 + 4z + 16 = 0, we find its roots using the quadratic formula: z = -4 16 - 64 2 = -4 -48 2 = -2 2 3 i The set S contains two complex numbers: z_1 = -2 + 2 3 i and z_2 = -2 - 2 3 i. We need to evaluate the sum _ z S |z + 3 i|^2, which is |z_1 + 3 i|^2 + |z_2 + 3 i|^2. For z_1 = -2 + 2 3 i: |z_1 + 3 i|^2 = |-2 + 2 3 i + 3 i|^2 = |-2 + 3 3 i|^2 |-2 + 3 3 i|^2 = (-2)^2 + (3 3 )^2 = 4 + 27 = 31 For z_2 = -2 - 2 3 i: |z_2 + 3 i|^2 = |-2 - 2 3 i + 3 i|^2 = |-2 - 3 i|^2 |-2 - 3 i|^2 = (-2)^2 + (- 3 )^2 = 4 + 3 = 7 Adding these values together: _ z S |z + 3 i|^2 = 31 + 7 = 38 Answer: 38