Question
If z_1, z_2, . . z_n are complex numbers such that |z_1 |= |z_2 |= . .= |z_n |=1, then |z_1+z_2+ . .+z_n | is equal to
BITSAT
Mathematics
Complex Number
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. |z_1 z_2 z_3 . . z_n |
- B. |z_1 |+ |z_2 |+ . .+ |z_n |
- C. | 1 z_1 + 1 z_2 + . .+ 1 z_n |
- D. n
Answer
C. | 1 z_1 + 1 z_2 + . .+ 1 z_n |
Step-by-step solution
|z_1 |= |z_2 |= |z_3 |= .= |z_n |=1 z_1 z _1=z_2 z _2=z_3 z _3= =z_n z _n=1 z _1= 1 z , z _2= 1 z _2 , z _3= 1 z _3 , , z _ n = 1 z _ n Now, |z_1+z_2+z_3+ .+z_n | = | z _1+ z _2+ + z _n | | z _1+ z _2+ z _3+ .+ z _n |= | 1 z_1 + 1 z_2 + 1 z_3 + + 1 z_n |
Related: Mathematics — Complex Number · All PYQ Banks