Complex Numbers
Complex Numbers
Allen Star Batch
Grade 11
Question:
A complex number $z$ satisfies the equation $|Z^2 - 9| + |Z^2 - 4| = 41$, then the true statements among the following are
$|Z + 3| + |Z - 3| = 10$
$|Z + 3| + |Z - 3| = 8$
Maximum value of $|Z|$ is $5$
Maximum value of $|Z|$ is $6$
Step-by-Step Solution
Key Concept: When distributing distinct objects into distinguishable groups of fixed sizes, divide by factorials of group sizes only if objects within groups are indistinguishable.
Since $S_1$ and $S_2$ each get 2 books and $S_3$ and $S_4$ each get 3 books, the required number of ways to distribute 10 distinct books is $\frac{10!}{2! \cdot 2! \cdot 3! \cdot 3!}$.
Correct Answer: 1,3