Quadrilateral formed by the points corresponding to the roots of `z^(4)-z^(3)+2z^(2)-z+1=0`is a

Prove that quadrilateral formed by the complex numbers which are roots of the equation z^(4) - z^(3) + 2z^(2) - z + 1 = 0 is an equailateral trapezium.

z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0 , then |z| is equal to

It is given the complex numbers z_(1) and z_(2) , |z_(1)| =2 and |z_(2)| =3 . If the included angle of their corresponding vectors is 60^(@) , then find value of |(z_(1) +z_(2))/(z_(1) -z_(2))|

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2 where lambda in R-{0}, then prove that points corresponding to z_1, z_2 and z_3 are collinear .

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2 w h e r e lambda in R-{0}, then prove that points corresponding to z_1, z_2a n dz_3 are collinear .

It is given that complex numbers z_1 and z_2 satisfy |z_1|=2 and |z_2|=3. If the included angled of their corresponding vectors is 60^0 , then find the value of |(z_1+z_2)/(z_1-z_2)| .

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = constant ne (|z_(1)-z_(2)|)

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = |z_(1)-z_(2)|

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_3 and "arg"[(z_4-z_1)//(z_2-z_1)]=pi//2 , the quadrilateral is

If 1 , z_1 , z_2 ,......., z_6 are the 7th roots of unity then the value of (2-z_1)(2-z_2)(2-z_3)(2-z_4)(2-z_5)(2-z_6)= (a) 63 b. 127 c. 32 d. 31