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

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

If log_(sqrt(3))((|z|^(2)-|z|+1)/(2+|z|))>2, then locate the region in the Argand plane which represents z

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|=

Let a complex number z|z| =1,. satisfy log _((1)/(sqrt2)) ((|z| +11)/((|z| -1) ^(2)))le 2. Then, the largest value of |z| is equal to "_______"

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