Complex Equations

JEE Main Mathematics · Complex Numbers · 11 questions, latest first

• Let the set of all values of k ∈ R such that the equation z(z̄+2+i)+k(2+3 i)=0, z ∈ C, has at least one solution, be the interval…20266 April, Shift 1 · Q4
• Let S={z ∈ C: z^2+4 z+16=0}. Then Σ_z ∈ S|z+√3 i|^2 is equal to:20264 April, Shift 2 · Q2
• Let S={z ∈ C: 4 z^2+z̄=0}. Then Σ_z ∈ S|z|^2 is equal to:202622 January, Shift 2 · Q5
• Let z ∈ C be such that (z^2+3 i)/(z-2+i)=2+3 i. Then the sum of all possible values of z^2 is20253 April, Shift 1 · Q4
• If α+i β and γ+i δ are the roots of x^2-(3-2 i) x-(2 i-2)=0, i=√-1, then α γ+β δ is equal to:202528 January, Shift 2 · Q4
• If α and β are the roots of the equation 2 z^2-3 z-2 i=0, where i=√-1, then 16 · Re((α^19+β^19+α^11+β^11)/(α^15+β^15)) ·…202524 January, Shift 1 · Q3
• Let α and β be the sum and the product of all the non-zero solutions of the equation (z̄)^2+|z|=0, z ∈ C. Then 4(α^2+β^2) is…20244 April, Shift 1 · Q2
• If z=x+i y, x y ≠ 0, satisfies the equation z^2+i z̄=0, then |z^2| is equal to:202430 January, Shift 1 · Q2
• Let S={z ∈ C: z̄=i(z^2+Re(z̄))}. Then Σ_z ∈ S|z|^2 is equal to202313 April, Shift 2 · Q2
• If for z=α+i β,|z+2|=z+4(1+i), then α+β and α β are the roots of the equation20238 April, Shift 1 · Q2
• Let a ≠ b be two non-zero real numbers. Then the number of elements in the set X={z ∈ C: Re(a z^2+b z)=a. and.Re(b z^2+a z)=b} is…20236 April, Shift 2 · Q3