Question
Let z=(1+i)(1+2 i)(1+3 i) (1+n i), where i= -1 . If |z|^ 2 =44200, then n is equal to \_\_\_\_
JEE Main
Mathematics
Complex Number
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
z = (1 + i)(1 + 2i)(1 + 3i) (1 + ni) where i = -1 |z|^2 = _ k=1 ^ n |1 + ki|^2 = _ k=1 ^ n (1 + k^2) Computing: (1+1)(1+4)(1+9)(1+16)(1+25) = 2 5 10 17 26 = 10 10 17 26 = 100 442 = 44200 Therefore n = 5
Related: Mathematics — Complex Number · All PYQ Banks