Complex Numbers
Complex Numbers
star_batch_jee_advanced_2025
Grade 11
Question:
Let $a = e^{2\pi i/1}, \lambda = a^k, \mu = a^{j}, \beta = a^2$. Then:
Re(λ + λ^2 + λ^3 + λ^4 + λ^5) = -\frac{1}{2}
(μ - β)(μ - β^2)(μ - β^3)…(μ - β^{10}) = 0
(i - β)(i - β^2)(i - β^3)…(i - β^{10}) = i
None of these
Step-by-Step Solution
Key Concept: Use multinomial coefficients to count arrangements when some items are identical.
The number of ways to arrange four items $C_1, C_2, C_3, C_4$ with values 2, 2, 2, 3 respectively is $\frac{9}{(2!)^3 \times 3} = \frac{9}{(2!)^3}$. This accounts for identical items using the multinomial coefficient.
Correct Answer: 1,2,3