The complex number satisfying $|z+\bar{z}|+|z-\bar{z}|=2$ and $|z+i|+|z-i|=2$ is/are:
Step-by-Step Solution
Key Concept: When objects are indistinguishable within types, divide the total permutations by the factorials of repetition counts to get the central binomial coefficient.
The number of permutations when there are repeated elements is given by $\frac{[2n]}{[n][n]} = ^{2n}C_n$, where $n$'s and $n$ $b$'s represent two types of identical objects. This formula counts distinct arrangements of $2n$ objects with $n$ of type A and $n$ of type B, yielding the central binomial coefficient.
Correct Answer: 1,2