Let A = {z ∈ C : |(z+1)/(z−1)| < 1} and B = {z ∈ C : arg((z−1)/(z+1)) = 2π/3}. Then A ∩ B Is
Let A: |(z+1)/(z−1)|<1 and B: arg((z−1)/(z+1))=2π/3 in the complex plane. Find A∩B by converting both conditions into geometric loci.
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The Remainder When (2021)^2023 Is Divided by 7 Is
Find the remainder when (2021)^2023 is divided by 7 — a modular arithmetic problem solved by reducing the base first, then finding a repeating power cycle.
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Let A=[0 -2,2 0], M=ΣA²ᵏ, N=ΣA²ᵏ⁻¹ (k=1 to 10): Find MN²
Find MN² for a 2×2 matrix A where M and N are sums of its even and odd powers. Solved by spotting that A² is a scalar multiple of the identity.
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Let A, B=A−I, ω=(√3i−1)/2: Count n With Aⁿ+(ωB)ⁿ=A+B
Given A^n + (ωB)^n = A + B for ω a complex cube root of unity, how many n in 1..100 satisfy it? JEE Main 2022 matrix and complex numbers problem.
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If sin²10°sin20°sin40°sin50°sin70°=α−1/16sin10°, Find 16+1/α
A five-term trigonometric product from JEE Main 2022, reduced step by step using complementary angles and the sin a cos a identity.