if `|z-2|=2|z-1|`, where z is a complex number, then prove `|z|^(2)= (4)/(3)` Re(z)

If |z-2|= "min" {|z-1|, |z-5|} , where z is a complex number, then

If z ^(2) + z + 1 = 0, where z is a complex number, then the value of (z + (1)/(z)) ^(2) + (z ^(2) + (1)/( z ^(2))) ^(2) + (z ^(3) + (1)/(z ^(3))) ^(2) +...( z ^(6) + (1)/(z ^(6)) )^(2) is

If z is a complex number such that Re (z) = Im (z), then :

If z^(2) + z + 1 = 0 where z is a complex num ber, then (z+(1)/(z))^(2)+(z^(2)+(1)/(z^(2)))^(2)+(z^(3)+(1)/(z^(3)))^(2) equal

If z is a complex number with absz=2 and arg(z)=(4pi)/3 . then Find overline z

The system of equation {:(|z+1-i|=2),(Re(z) ge 1):}} , where z is a complex number has

If z is a complex number such that z+ |z|=8 +12i then the value of |z^2| is

If z_(1) and z_(2) are non -zero complex numbers, then show that (z_(1) z_(2))^(-1)=z_(1)^(-1) z_(2)^(-1)

If the conjugate of a complex number z is (1)/(i-1) , then z is

If z=x+iy is a complex number such that |z|=Re(iz)+1 , then the locus of z is