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)` is

On the complex plane locus of a point z satisfying the inequality 2<=|z-1|<3 denotes

The locus of z satisfying the inequality log_(1//3)|z+1|gtlog_(1//3)|z-1|

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

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

The locus of z satisfying the inequality |(z+2i)/(2z+1)|<1, where z=x+iy, is :

If z be a complex number satisfying z^4+z^3+2z^2+z+1=0 then absz is equal to

Locus of z in the argand plane if z satisfies the condition cot^(-1)(log_(3)(|2z+1|))>cot^(-1)(log_(3)(|2z+1|))

Show that complex numbers z_1=-1+5i and z_2=-3+2i on the argand plane.