De Moivre's Theorem

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

• Let S={z ∈ C: z^2+√6 i z-3=0}. Then Σ_z ∈ S z^8 is equal to:20266 April, Shift 2 · Q3
• If z=(√3)/2+i/2, i=√-1, then (z^201-i)^8 is equal to202623 January, Shift 2 · Q4
• Let α, β be the roots of the equation x^2-√6 x+3=0 such that Im(α)>Im(β). Let a, b be integers not divisible by 3 and n be a…202429 January, Shift 2 · Q22
• Let α, β be the roots of the equation x^2-√2 x+2=0. Then α^14+β^14 is equal to202313 April, Shift 2 · Q3
• Let α, β be the roots of the quadratic equation x^2+√6 x+3=0. Then (α^23+β^23+α^14+β^14)/(α^15+β^15+α^10+β^10) is equal to202312 April, Shift 1 · Q2
• The value of ((1+ sin (2 π)/9+i cos (2 π)/9)/(1+ sin (2 π)/9-i cos (2 π)/9))^3 is202324 January, Shift 2 · Q63
• Let p, q ∈ R and (1-√3 i)^200=2^199(p+i q), i=√-1 Then p+q+q^2 and p-q+q^2 are roots of the equation.202324 January, Shift 1 · Q63