Question
Let S= \ z C : 4 z^ 2 + z =0 \ . Then _ z S |z|^ 2 is equal to:
JEE Main
Mathematics
Complex Number
2026
JEE Main 2026 (22 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 5 64
- B. 1 16
- C. 3 16
- D. 7 64
Answer
C. 3 16
Step-by-step solution
Let z=x+iy. From 4z^2+ z =0, separating real and imaginary parts: Real: 4x^2-4y^2+x=0, Imaginary: y(8x-1)=0. Case 1: y=0 x(4x+1)=0 z=0 or z=- 1 4 . Case 2: x= 1 8 1 16 -4y^2+ 1 8 =0 y^2= 3 64 . So |z|^2= 1 64 + 3 64 = 1 16 . |z|^2=0+ 1 16 + 1 16 + 1 16 = 3 16
Related: Mathematics — Complex Number · All PYQ Banks