Argand Plane & Geometry: JEE Questions & Solutions

Let z be the complex number satisfying |z - 5| ≤ 3 and having maximum positive principal argument. Then 34 | (5z - 12)/(5iz + 16) |² is…

Let S = {z: 3 ≤ |2z - 3(1+i)| ≤ 7} be a set of complex numbers. Then min_(z ∈ S) | z + 1/2(5+3i) | is equal to:

Let S={z∈ℂ:|(z-6i)/(z-2i)|=1 and |(z-8+2i)/(z+2i)|=3/5}. Then Σ_(z∈ S)|z|² is equal to

Let z be a complex number such that |z-6|=5 and |z+2-6i|=5. Then the value of z³+3z²-15z+141 is equal to:

Let A={z∈ℂ:|z-2|≤ 4} and B={z∈ℂ:|z-2|+|z+2|=5}. Then the maximum value of |z₁-z₂|, where z₁∈ A and z₂∈ B, is:

Let the curve z(1 + i) + z(1 - i) = 4, z ∈ ℂ, divide the region |z - 3| ≤ 1 into two parts of areas α and β. Then |α - β| equals:

Let | (z - i)/(2z + i) | = 1/3, z ∈ ℂ, be the equation of a circle with center at C. If the area of the triangle, whose vertices are at the…

Let |z₁ - 8 - 2i| ≤ 1 and |z₂ - 2 + 6i| ≤ 2, where z₁, z₂ ∈ ℂ. Then the minimum value of |z₁ - z₂| is:

Let z be a complex number such that |z| = 1. If (2 + k² z)/(k + z) = kz, k ∈ ℝ, then the maximum distance of k + ik² from the circle |z -…

If z₁, z₂, z₃ ∈ ℂ are the vertices of an equilateral triangle, whose centroid is z₀, then Σ_(k=1)³ (z_k - z₀)² is equal to

Let A = { z ∈ ℂ: |z - 2 - i| = 3 }, B = { z ∈ ℂ: Re(z - iz) = 2 }, and S = A ∩ B. Then Σ_(z ∈ S) |z|² is equal to.

If the locus of z ∈ ℂ, such that Re ( (z - 1)/(2z + i)) + Re ( (z - 1)/(2 z - i)) = 2, is a circle of radius r and center (a, b), then…

If S = {z ∈ ℂ: |z-i| = |z+i| = |z-1|}, then n(S) is:

Let S = {z ∈ ℂ: |z - 1| = 1 and (√2 - 1)(z + z) - i(z - z) = 2√2}. Let z₁, z₂ ∈ S be such that |z₁| = max_(z ∈ S) |z| and |z₂| = min_(z ∈…

The area of the region S = { z ∈ ℂ: |z - 1| ≤ 2, (z + z) + i(z - z) ≤ 2, Im(z) ≥ 0 } is:

Let z be a complex number such that the real part of (z-2i)/(z+2i) is zero. Then, the maximum value of |z-(6+8i)| is equal to:

Let z₁ = 2 + 3i and z₂ = 3 + 4i. The set S = { z ∈ ℂ: |z - z₁|² - |z - z₂|² = |z₁ - z₂|² } represents a:

Let z be a complex number such that (|z - 2i|)/(|z + i|) = 2, z ≠ -i. Then z lies on the circle of radius 2 and centre:

Let α = 8 - 14i, A = { z ∈ ℂ: (α z - α z)/(z² - (z)² - 112i) = 1 } and B = { z ∈ ℂ: |z + 3i| = 4 }. Then Σ_(z ∈ A ∩ B) (Re z - Im z) is…

For all z ∈ ℂ on the curve C₁: |z| = 4, let the locus of the point z + 1/z be the curve C₂. Then:

Let C be the circle in the complex plane with centre z₀ = 1/2(1 + 3i) and radius r = 1. Let z₁ = 1 + i and the complex number z₂ be outside…