Cube Roots of Unity

JEE Main Mathematics · Complex Numbers · 7 questions, latest first

• Let α=(-1+i √3)/2 and β=(-1-i √3)/2, i=√-1. If (7-7 α+9 β)^20+(9+7 α-7 β)^20+(-7+9 α+7 β)^20+(14+7 α+7 β)^20=m^10, then m is ____202622 January, Shift 1 · Q21
• If x^2+x+1=0, then the value of (x+1/x)^4+(x^2+1/x^2)^4+(x^3+1/x^3)^4+…+(x^25+1/(x^25))^4 is:202621 January, Shift 1 · Q4
• Let α be a solution of x^2+x+1=0, and for some a and b in R, [4, a, b] [1, 16, 13; -1, -1, 2; -2, -14, -8] = [0, 0, 0]. If…20258 April, Shift 2 · Q5
• If α is a root of the equation x^2+x+1=0 and Σ_k=1^n(α^k+1/(α^k))^2=20, then n is equal to ____.20254 April, Shift 2 · Q21
• Let integers a, b ∈[-3,3] be such that a+b ≠ 0. Then the number of all possible ordered pairs (a, b), for which |(z-a)/(z+b)|=1…202529 January, Shift 2 · Q21
• If z is a complex number, then the number of common roots of the equations z^1985+z^100+1=0 and z^3+2 z^2+2 z+1=0, is equal to202430 January, Shift 2 · Q2
• If α satisfies the equation x^2+x+1=0 and (1+α)^7=A+B α+C α^2, A, B, C ≥ 0, then 5(3 A-2 B-C) is equal to ____.202427 January, Shift 1 · Q21