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

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

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

z_1, z_2, z_3,z_4 are distinct complex numbers representing the vertices of a quadrilateral A B C D taken in order. If z_1-z_4=z_2-z_3a n d"a r g"[(z_4-z_1)//(z_2-z_1)]=pi//2 , the quadrilateral is a. rectangle b. rhombus c. square d. trapezium

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 represent three vertices of an equilateral triangle in argand plane then show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)=0

If |z_1/z_2|=1 and arg (z_1z_2)=0 , then a. z_1 = z_2 b. |z_2|^2 = z_1*z_2 c. z_1*z_2 = 1 d. none of these

In the complex plane, the vertices of an equlitateral triangle are represented by the complex numbers z_(1),z_(2) and z_(3) prove that, (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

P(z_1),Q(z_2),R(z_3)a n dS(z_4) are four complex numbers representing the vertices of a rhombus taken in order on the complex lane, then which one of the following is/ are correct? (z_1-z_4)/(z_2-z_3) is purely real a m p(z_1-z_4)/(z_2-z_3)=a m p(z_2-z_4)/(z_3-z_4) (z_1-z_3)/(z_2-z_4) is purely imaginary It is not necessary that |z_1-z_3|!=|z_2-z_4|

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

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 =