Complex Numbers
Complex Numbers
Allen Star Batch
Grade 11
Question:
If the roots $Z_1, Z_2, Z_3$ of the equation $Z^3 - Z^2 + mZ - 1 = 0$ lie on $|Z| = 1$ and $|(Z_1 + 3)(Z_2 + 3)(Z_3 + 3)| = 10$, then $\lambda = $ ____.
Step-by-Step Solution
Key Concept: When objects are indistinguishable, divide by the number of permutations of those objects to avoid overcounting.
The first rook can be placed in 64 ways on a standard chessboard. The second rook cannot be in the same row or column, leaving $7 \times 7 = 49$ positions. Since the order of placement doesn't matter, divide by $2!$ to get $\frac{64 \times 49}{2} = 1568$ ways.
Correct Answer: 4