`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 represent the vertices of a rhombus in anticlockwise order, then

If the complex numbers z_(1),z_(2),z_(3) represents the vertices of an equilaterla triangle such that |z_(1)|=|z_(2)|=|z_(3)| , show that z_(1)+z_(2)+z_(3)=0

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

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

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|

In the Argand plane the distinct roots of 1+z+z^3+z^4=0 (z is a complex number) represent vertices of

If z_1,z_2 and z_3,z_4 are two pairs of conjugate complex numbers, then arg(z_1/z_4)+arg(z_2/z_3) equals

If A(z_1), B(z_2), C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_3-2z_1)/(z_3-z_2)) is equal to

The complex numbers z_1,z_2 and z_3 satisfying (z_1-z_3)/(z_2-z_3)=(1-isqrt3)/2 are the verticles of a triangle which is:

If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of possible values of z is