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 - 125iz + 16 |^2 is equal to:

Let S = z: 3 |2z - 3(1+i)| 7 be a set of complex numbers. Then z S | z + 12(5+3i) | is equal to:

Let S= z C: | z-6iz-2i |=1 and | z-8+2iz+2i |= 35. Then 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 z^3+3z^2-15z+14 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 and. Then | - | equals:

Let z - iz - i = 13, z C, be the equation of a circle with center at C. If the area of the triangle, whose vertices are at the points (0,…

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 + kzk + z = kz, k R, then the maximum distance of k + ik^2 from the circle |z - (1 + 2i)|…

If z1, z2, z3 C are the vertices of an equilateral triangle, whose centroid is z0, then k=1^3 (zk - 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 z S |z|^2 is equal to

If the locus of z C, such that Re ( z - 12z + i) + Re ( z - 12 z - i) = 2, is a circle of radius r and center (a, b), then 15abr^2 is equal…

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) = ( z - z) = 2 2. Let z1, z2 S be such that |z1| = z S |z| and |z2| = z S |z|. Then |z1 -…

The area of the region S = z C: |z - 1|^2 4, z + z 2, Im(z) 0 is:

Let z be a complex number such that the real part of z-2iz+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 = 8 - 14i, A = z C: |z^2 - ^2| = |z^2 - ^2|, and B = z C: |z + 3i| = 4. Then z A B ( Re z - Im z) is equal to:

For all z C on the curve C such that |z| = 1, let the locus of the point z + 1z be the curve C1. Then:

Let C be the circle in the complex plane with centre z0 = 12(1 + 3i) and radius r = 1. Let z1 = 1 + i and the complex number z2 be outside…