Circles in the Complex Plane

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

• Let the circles C_1:|z|=r and C_2:|z-3-4 i|=5, z ∈ C, be such that C_2 lies within C_1. If z_1 moves on C_1, z_2 moves on C_2 and…20262 April, Shift 2 · Q2
• Let z be a complex number such that |z-6|=5 and |z+2-6 i|=5. Then the value of z^3+3 z^2-15 z+141 is equal to202628 January, Shift 1 · Q4
• Let S={z ∈ C:|(z-6 i)/(z-2 i)|=1. and.|(z-8+2 i)/(z+2 i)|=3/5}. Then Σ_z ∈ S|z|^2 is equal to202624 January, Shift 1 · Q3
• Let S={z: 3 ≤|2 z-3(1+i)| ≤ 7} be a set of complex numbers. Then min_z ∈ S|(z+1/2(5+3 i))| is equal to:202623 January, Shift 1 · Q4
• Let A={z ∈ C:|z-2-i|=3}, B={z ∈ C: Re(z-i z)=2} and S=A ∩ B. Then Σ_z ∈ S|z|^2 is equal to ____20254 April, Shift 1 · Q21
• Let |z_1-8-2 i| ≤ 1 and |z_2-2+6 i| ≤ 2, z_1, z_2 ∈ C. Then the minimum value of |z_1-z_2| is:202529 January, Shift 1 · Q2
• Let |(z̄-i)/(2 z̄+i)|=1/3, z ∈ C, be the equation of a circle with center at C. If the area of the triangle, whose vertices are…202523 January, Shift 1 · Q3
• Let z be a complex number such that the real part of (z-2 i)/(z+2 i) is zero. Then, the maximum value of |z-(6+8 i)| is equal to20249 April, Shift 2 · Q2
• Let S={z ∈ C:|z-1|=1 and (√2-1)(z+z̄)-i(z-z̄)=2 √2}. Let z_1, z_2 ∈ S be such that |z_1|= max_Z ∈ S|z| and |z_2|= min_Z ∈ S|z|.…20241 February, Shift 1 · Q1
• Let w=z z̄+k_1 z+k_2 i z+λ(1+i), k_1, k_2 ∈ R. Let Re(w)=0 be the circle C of radius 1 in the first quadrant touching the line…202313 April, Shift 1 · Q21
• Let C be the circle in the complex plane with centre z_0=1/2(1+3 i) and radius r=1. Let z_1=1+i and the complex number z_2 be…202312 April, Shift 1 · Q7
• For α, β, z ∈ C and λ>1, if √(λ-1) is the radius of the circle |z-α|^2+|z-β|^2=2 λ, then |α-β| is equal to ____.20236 April, Shift 2 · Q21
• If the center and radius of the circle |(z-2)/(z-3)|=2 are respectively (α, β) and γ, then 3(α+β+γ) is equal to20231 February, Shift 1 · Q62
• Let z be a complex number such that |(z-2 i)/(z+i)|=2, z ≠-i. Then z lies on the circle of radius 2 and centre202325 January, Shift 2 · Q63