If $z_1 = a_1 + ib_1$ and $z_2 = a_2 + ib_2$ are complex numbers such that $|z_1| = 1$, $|z_2| = 2$ and $\text{Re}(z_1z_2) = 0$ then the pair of complex numbers $w_1 = a_1 + \frac{ia_2}{2}$ and $w_2 = 2b_1 + ib_2$ satisfy
Step-by-Step Solution
Key Concept: Recognize that permutations and combinations yield distinct numerical results based on whether order matters.
The four options are evaluated: (A) $\binom{6}{1} \binom{2}{2} = 5! \cdot 3 = (5!)^3$, (B) $\binom{6}{1} \cdot 9!$, (C) $(6+1)! \cdot 4!$, and (D) $\binom{10}{4}$. These represent different combinatorial values related to selection and arrangement problems.
Correct Answer: 1,2,3,4