Question
If |z_1 |=2, |z_2 |=3, |z_3 |=4 and |2 z_1+3 z_2+4 z_3 |= 4 , then absolute value of 8 z_2 z_3+27 z_3 z_1+ 64 z_1 z_2 equals
BITSAT
Mathematics
Complex Number
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 24
- B. 48
- C. 72
- D. 96
Answer
D. 96
Step-by-step solution
|8 z_2 z_3+27 z_3 z_1+64 z_1 z_2 |= |z_1 | |z_2 | |z_3 | | 8 z_1 + 27 z_2 + 64 z_3 | =(2)(3)(4) | 8 z _1 |z_1 |^2 + 27 z _2 |z_2 |^2 + 64 z _3 |z_3 |^2 | =24 |2 z _1+3 z _2+4 z _3 | =24 | 2 z_1+3 z_2+4 z_3 | =24 |2 z_1+3 z_2+4 z_3 |=(24)(4)=96
Related: Mathematics — Complex Number · All PYQ Banks