Suppose `z_(1),z_(2)andz_(3)` are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If `z_(1)=1+isqrt3` then find `z_(2)andz_(3)`.

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals:

If z_(1),z_(2),z_(3) are the vertices of a parallelogram, then the fourth vertex z_(4) opposite to z_(2) is _____

If the complex numbers z_(1), z_(2)" and "z_(3) denote the vertices of an isoceles triangle, right angled at z_(1), " then "(z_(1)-z_(2))^(2)+(z_(1)-z_(3))^(2) is equal to

Let the complex numbers z_(1),z_(2),z_(3)" and "z_(4) denote the vertices of a square taken in order. If z_(1)=3+4i" and "z_(3)=5+6i , then the other two vertices z_(2)" and "z_(4) are respectively

If the points A(z),B(-z),a n dC(1-z) are the vertices of an equilateral triangle A B C , then (a)sum of possible z is 1/2 (b)sum of possible z is 1 (c)product of possible z is 1/4 (d)product of possible z is 1/2

In A B C ,A(z_1),B(z_2),a n dC(z_3) are inscribed in the circle |z|=5. If H(z_n) be the orthocenrter of triangle A B C , then find z_ndot

If z_(1)=3-4i , z_(2)=2+i find bar(z_(1)z_(2))

If z_0 is the circumcenter of an equilateral triangle with vertices z_1, z_2, z_3 then z_1^2+z_2^2+z_3^2 is equal to

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot