Loci in the Argand Plane

JEE Main Mathematics · Complex Numbers · 14 questions, latest first

• The number of values of z ∈ C, satisfying the equations |z-(4+8 i)|=√10 and |z-(3+5 i)|+|z-(5+11 i)|=4 √5, is:20268 April, Shift 2 · Q2
• Let A={z ∈ C:|z-2| ≤ 4} and B={z ∈ C:|z-2|+|z+2|=5}. Then the max {|z_1-z_2|: z_1 ∈ A. and.z_2 ∈ B} is:202628 January, Shift 2 · Q3
• If the locus of z ∈ C, such that Re((z-1)/(2 z+i))+Re((z̄-1)/(2 z̄-i))=2, is a circle of radius r and center (a, b), then (15…20257 April, Shift 2 · Q4
• Among the statements (S1): The set {z ∈ C-{-i}:|z|=1. and (z-i)/(z+i) is purely real } contains exactly two elements, and (S2):…20257 April, Shift 1 · Q2
• Let the curve z(1+i)+z̄(1-i)=4, z ∈ C, divide the region |z-3| ≤ 1 into two parts of areas α and β. Then |α-β| equals:202522 January, Shift 2 · Q3
• The sum of the square of the modulus of the elements in the set {z=a+ib: a, b ∈ Z, z ∈ C,|z-1| ≤ 1,|z-5| ≤|z-5 i|} is ____.20249 April, Shift 1 · Q22
• Let S_1={z ∈ C:|z| ≤ 5}, S_2={z ∈ C: Im((z+1-√3 i)/(1-√3 i)) ≥ 0} and S_3={z ∈ C: Re(z) ≥ 0}. Then the area of the region S_1 ∩…20245 April, Shift 2 · Q3
• The area (in sq. units) of the region S={z ∈ C:|z-1| ≤ 2;(z+z̄)+i(z-z̄) ≤ 2, Im(z) ≥ 0} is20244 April, Shift 2 · Q2
• Let P={z ∈ C:|z+2-3 i| ≤ 1} and Q={z ∈ C: z(1+i)+z̄(1-i) ≤-8}. Let in P ∩ Q, |z-3+2 i| be maximum and minimum at z_1 and z_2…20241 February, Shift 1 · Q22
• If S={z ∈ C:|z-i|=|z+i|=|z-1|}, then, n(S) is:202427 January, Shift 1 · Q3
• Let S={z=x+i y: (2 z-3 i)/(4 z+2 i). is a real number }. Then which of the following is NOT correct?202310 April, Shift 2 · Q3
• For all z ∈ C on the curve C_1:|z|=4, let the locus of the point z+1/z be the curve C_2. Then:202331 January, Shift 1 · Q63
• Let α=8-14 i, A={z ∈ C: (α z-ᾱ z̄)/(z^2-(z̄)^2-112 i)=1} and B={z ∈ C:|z+3 i|=4}. Then Σ_z ∈ A ∩ B(Re z-Im z) is equal to ____.202329 January, Shift 2 · Q82
• Let z_1=2+3 i and z_2=3+4 i. The set S={z ∈ C:|z-z_1|^2-|z-z_2|^2=|z_1-z_2|^2} represents a202325 January, Shift 1 · Q61