Find the relation if `z_1, z_2, z_3, z_4` are the affixes of the vertices of a parallelogram taken in order.

The points, z_1,z_2,z_3,z_4, in the complex plane are the vertices of a parallelogram taken in order, if and only if (a) z_1+z_4=z_2+z_3 (b) z_1+z_3=z_2+z_4 (c) z_1+z_2=z_3+z_4 (d) None of these

If z_1, z_2, z_3, z_4 represent the vertices of a rhombus in anticlockwise order, then

If z_1, z_2, z_3 be the affixes of the vertices A, B and 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 =

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

If A(z_1),B(z_2),C(z_3) and D(z_4) be the vertices of the square ABCD then

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

Given that the complex numbers which satisfy the equation | z bar z ^3|+| bar z z^3|=350 form a rectangle in the Argand plane with the length of its diagonal having an integral number of units, then area of rectangle is 48 sq. units if z_1, z_2, z_3, z_4 are vertices of rectangle, then z_1+z_2+z_3+z_4=0 rectangle is symmetrical about the real axis a r g(z_1-z_3)=pi/4or(3pi)/4

If (x_(1),y_(1),z_(1)) , (x_(2),y_(2),z_(2)) , (x_(3) ,y_(3),z_(3)) and (x_(4) , y_(4) , z_(4)) be the consecutive vertices of a parallelogram, show that x_(1)+x_(3)=x_(2)+x_(4),y_(1)+y_(3)=y_(2)+y_(4) and z_(1)+z_(3)=z_(2)+z_(4) .

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle then prove that z_1^2+z_2^2+z_3^2=3z_0^2

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.