[" Let S be the set of complex number "z" which satisfy "log_(1/3){log_(1/2)(|z|^(2)+4|z|+3)}<0" ,then "" Sis (where i "],[=sqrt(-1))" : "]

Let S be the set of complex number a which satisfyndof log_((1)/(3)){log_((1)/(2))(|z|^(2)+4|z|+3)}<0, then s is (where i=sqrt(-1))

Let z_(1)=2+3iandz_(2)=3+4i be two points on the complex plane . Then the set of complex number z satisfying |z-z_(1)|^(2)+|z-z_(2)|^(2)=|z_(1)-z_(2)|^(2) represents -

For a complex z , let Re(z) denote the real part of z . Let S be the set of all complex numbers z satisfying z^(4)- |z|^(4) = 4 iz^(2) , where I = sqrt(-1) . Then the minimum possible value of |z_(1)-z_(2)|^(2) where z_(1),z_(2) in S with Re (z_(1)) gt 0 and Re (z_(2)) lt 0 , is ....

For a complex number z ,let Re(z) denote the real part of z . Let S be the set of all complex numbers z satisfying z^(4)-|z|^(4)=4iz^(2) ,where i=sqrt(-1) . Then the minimum possible value of |z_(1)-z_(2)|^(2) ,where, z_(1),z_(2) in S with Re(z_(1))>0 and Re(z_(2))<0, is

Let C_1 and C_2 are concentric circles of radius 1and 8/3 respectively having centre at (3,0) on the argand plane. If the complex number z satisfies the inequality log_(1/3)((|z-3|^2+2)/(11|z-3|-2))>1, then (a) z lies outside C_(1) but inside C_(2) (b) z line inside of both C_(1) and C_(2) (c) z line outside both C_(1) and C_(2) (d) none of these

Let C_(1) and C_(2) are concentric circles of radius 1 and (8)/(3) respectively having centre at (3,0) on the argand plane.If the complex number z satisfies the inequality log_((1)/(3))((|z-3|^(2)+2)/(11|z-3|-2))>1, then