Question
If z= 3 2 + i 2 , i= -1 , then (z^ 201 -i )^ 8 is equal to
JEE Main
Mathematics
Complex Number
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 1
- B. 256
- C. -1
- D. 0
Answer
B. 256
Step-by-step solution
z = 3 2 + i 2 = e^ i /6 . z^ 201 = e^ i 201 /6 = e^ i 33.5 = e^ i(33 + /2) . Since e^ i 33 = e^ i = -1, we get z^ 201 = -1 e^ i /2 = -i. z^ 201 - i = -i - i = -2i. (z^ 201 - i)^8 = (-2i)^8 = 2^8 i^8 = 256 1 = 256.
Related: Mathematics — Complex Number · All PYQ Banks