Difference between the square of the least and the square of the greatest values of $|z|$, where $z = e^{i2\theta} \sin\theta + \cos\theta - \cos(\phi + R)$ is ____.
Step-by-Step Solution
Key Concept: Convert inequality constraints using dummy variables, then subtract invalid boundary cases.
A customer buys 4 ice cream types (a, b, c, d) with $0 < a + b + c + d \leq 10$. Using a dummy variable $k$ such that $a + b + c + d + k = 10$, the number of non-negative integer solutions is $\binom{10+5-1}{5-1} = \binom{14}{4} = 1001$. Subtracting the case where $a + b + c + d = 10$ (which is invalid): $1001 - 1 = 1000$. Therefore $\frac{k}{100} = 10$.
Correct Answer: 1