Question
Let z be a complex number with non-zero imaginary part. If 2 + 3 z + 4 z 2 2 - 3 z + 4 z 2 is a real number, then the value of z 2 is ______.
JEE Advanced
Mathematics
Complex Number
2022
JEE Advanced 2022 (Paper 1)
JEE Advanced Mathematics Question (2022) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
Let α = 4 z 2 + 3 z + 2 4 z 2 - 3 z + 2 = 1 + 6 z 4 z 2 - 3 z + 2 ⇒   α = 1 + 6 2 2 z + 1 z - 3 ∵   α ∈ R then 2 z + 1 z ∈ R ⇒ 2 z + 1 z = 2 z ¯ + 1 z ¯ ⇒ 2 z - z ¯ - z - z ¯ z 2 = 0 ⇒ z - z ¯ 2 - 1 z 2 = 0 ∵   z ≠ z ¯ (given) So z 2 = 1 2
Related: Mathematics — Complex Number · All PYQ Banks