Question
Let z be the complex number satisfying |z-5| 3 and having maximum positive principal argument. Then 34 | 5 z-12 5 i z+16 |^ 2 is equal to :
JEE Main
Mathematics
Complex Number
2026
JEE Main 2026 (21 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 26
- B. 12
- C. 20
- D. 16
Answer
C. 20
Step-by-step solution
The region |z - 5| 3 is a disk centered at (5, 0) with radius 3. Maximum positive principal argument from origin occurs at the tangent point from origin to the circle. = 3 5 , = 4 5 . The tangent point is the foot of perpendicular from (5,0) to the line 3x - 4y = 0, giving z = 16 5 + 12 5 i. 5z - 12 = 4 + 12i |5z - 12|^2 = 160 5iz + 16 = 4 + 16i |5iz + 16|^2 = 272 34 | 5z-12 5iz+16 |^2 = 34 160 272 = 34 10 17 = 20.
Related: Mathematics — Complex Number · All PYQ Banks