if `z+1/z=1` then `z^4+1/(z^4)=`

z = (1+i)/(1-i) then z^4 = .......... .

If z=x+iy such that |z+1|=|z-1| and arg((z-1)/(z+1))=(pi)/(4) then

The complex number z satisfying |z+1|=|z-1| and arg (z-1)/(z+1)=pi/4 , is

If |z_1|=1,|z_2|=1 then prove that |z_1+z_2|^2+|z_1-z_2|^2 =4.

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

If z_(1) satisfies |z-1|=1 and z_(2) satisfies |z-4i|=1 , then |z_(1)-z_(2)|_("max")-|z_(1)-z_(2)|_("min") is equal to ___________

Let four points z_(1),z_(2),z_(3),z_(4) be in complex plane such that |z_(2)|= 1, |z_(1)|leq 1 and |z_(3)| le 1 . If z_(3) = (z_(2)(z_(1)-z_(4)))/(barz_(1)z_(4)-1) , then |z_(4)| can be

Let four points z_(1),z_(2),z_(3),z_(4) be in complex plane such that |z_(2)|= 1, |z_(1)|leq 1 and |z_(3)| le 1 . If z_(3) = (z_(2)(z_(1)-z_(4)))/(barz_(1)z_(4)-1) , then |z_(4)| can be (a) 2 (b) 2/5 (c) 1/3 (d) 5/2