The points, `z_1,z_2,z_3,z_4,` in the complex plane are the vartices 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

The points z_(1)z_(2)z_(3)z_(4) in the complex plane are the vertices of a parallelgram taken in order if and only if :

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 a m p(z_1z_2)=0a n d|z_1|=|z_2|=1,t h e n z_1+z_2=0 b. z_1z_2=1 c. z_1=z _2 d. none of these

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 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 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)" and "z_(3) are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are z_(1),z_(2)" and "z_(3) taken in order is

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 =

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.