Question
For a non-zero complex number z, let (z) denote the principal argument of z, with - < (z) . Let be the cube root of unity for which 0 < ( ) < . Let = ( _ n=1 ^ 2025 (- )^n ). Then the value of 3 is ___________
JEE Advanced
Mathematics
Complex Number
2025
JEE Advanced 2025 (Paper 2)
JEE Advanced Mathematics Question (2025) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
aligned & = (- + ^2- ^3+ +(- )^ 2025 ) \\ & = ( - ((- )^ 2025 -1 ) - -1 ) \\ & = ( - - -1 (-2) ) \\ & = ( -2 +1 ) \\ & = ( -2 - ^2 ) \\ & = ( 2 ) \\ & = (2 ^2 ) \\ & = -2 3 \\ & 3 =-2 aligned
Related: Mathematics — Complex Number · All PYQ Banks