JEE Main 2026 Mathematics question
Let z₁,z₂∈ℂ be the distinct solutions of the equation z²+4z−(1+12i)=0. Then |z₁|²+|z₂|² is equal to:
Answer: (D)
Solution
√(5+12i)=3+2i, giving z₁=1+2i, z₂=−5−2i. |z₁|²=5, |z₂|²=29. Sum=34.
Let z₁,z₂∈ℂ be the distinct solutions of the equation z²+4z−(1+12i)=0. Then |z₁|²+|z₂|² is equal to:
√(5+12i)=3+2i, giving z₁=1+2i, z₂=−5−2i. |z₁|²=5, |z₂|²=29. Sum=34.