If `z_1, z_2, z_3` be the affixes of the vertices `A, B Mand C` of a triangle having centroid at G such ;that `z = 0` is the mid point of AG then `4z_1 + Z_2 + Z_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, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

Let z_1, z_2a n dz_3 represent the vertices A ,B ,a n dC of the triangle A B C , respectively, in the Argand plane, such that |z_1|=|z_2|=|z_3|=5. Prove that z_1sin2A+z_2sin2B+z_3sin2C=0.

Let the altitudes from the vertices A, B and Cof the triangle e ABCmeet its circumcircle at D, E and F respectively and z_1, z_2 and z_3 represent the points D, E and F respectively. If (z_3-z_1)/(z_2-z_1) is purely real then the triangle ABC is

On the Argand plane z_1, z_2a n dz_3 are respectively, the vertices of an isosceles triangle A B C with A C=B C and equal angles are thetadot If z_4 is the incenter of the triangle, then prove that (z_2-z_1)(z_3-z_1)=(1+sectheta)(z_4-z_1)^2dot

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled trianglewith right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

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

Let z_1, z_2, z_3 be three complex numbers and a ,b ,c be real numbers not all zero, such that a+b+c=0a n da z_1+b z_2+c z_3=0. Show that z_1, z_2,z_3 are collinear.

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) .