The number of solution(s) of the equation $z^2 - z - |z|^2 - \frac{64}{|z|^3} = 0$ is ___________.
Step-by-Step Solution
Key Concept: Nested binomial expansions simplify when using the alternating sum form and distributing coefficients correctly.
Option (B): $^6C_3 [(3^7 - ^1C_1(2)^7 + ^2C_2] = 20 \times [2187 - 384 + 3] = 36120$. This uses binomial expansion with careful tracking of signs and indices in the nested sum.
Correct Answer: 1