If `log_(1/2)((|z|^2+2|z|+4)/(2|z|^2+1))<0` then the region traced by z is ___

If log_(sqrt3) |(|z|^2 -|z| +1|)/(|z|+2)|<2 then locus of z is

If log_(sqrt3) ((|z|^(2)-|z|+1)/(2+|z|)) gt 2 , then the locus of z is

If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2 , then the locus of z is

If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2 , then the locus of z is

If log_(tan30^@)[(2|z|^(2)+2|z|-3)/(|z|+1)] lt -2 then |z|=

If log_(tan30^@)[(2|z|^(2)+2|z|-3)/(|z|+1)] lt -2 then |z|=

If log_(sqrt(3))|(|z|^(2)-|z|+1|)/(|z|+2)|<2 then locus of z is

The focus of the complex number z in argand plane satisfying the inequality log_((1)/(2))((|z-1|+4)/(3|z-1|-2))>1(where|z-1|!=(2)/(3))