If `z=(4)/(5)(z+10)`,then `z=?`

If z=e^((2pi i)/5) , then 1+z+z^(2)+z^(3)+5z^(4)+4z^(5)+4z^(6)+4z^(7)+4z^(8)+5z^(9)=

Let z in C be such that |z| lt 1 .If omega =(5+3z)/(5(1-z) then

If |(z-25)/(z-1)| = 5 , the value of |z| is -

If |(z-25)/(z-1)| = 5 , the value of |z| is -

z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0 , then |z| 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 (a) 2 (b) 2/5 (c) 1/3 (d) 5/2

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

Let z be a complex number such that |(z-5i)/(z+5i)|=1 , then show that z is purely real

For a complex number Z, if arg Z=(pi)/(4) and |Z+(1)/(Z)|=4 , then the value of ||Z|-(1)/(|Z|)| is equal to