Given that `|z-a|=a`, and `|b-a|=|b-2a| = a` where z is a point in the Argand's plane, then the complex number b can be

Locate the region in the Argand plane for the complex number z satisfying |z-4| < |z-2|.

Let A,B,C be three collinear points which are such that AB.AC=1 and the points are represented in the Argand plane by the complex numbers, 0, z_(1) and z_(2) respectively. Then,

Let A,B,C be three collinear points which are such that AB.AC=1 and the points are represented in the Argand plane by the complex numbers, 0, z_(1) and z_(2) respectively. Then,

Let 3-i and 2+i be affixes of two points A and B in the Argand plane and P represents the complex number z=x+iy . Then, the locus of the P if |z-3+i|=|z-2-i| , is

Let 3-i and 2+i be affixes of two points A and B in the Argand plane and P represents the complex number z=x+iy . Then, the locus of the P if |z-3+i|=|z-2-i| , is

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

If |z-1|=1, where z is a point on the argand plane, show that (z-2)/(z)=i tan (argz),where i=sqrt(-1).

If |z-1|=1, where z is a point on the argand plane, show that (z-2)/(z)=i tan (argz),where i=sqrt(-1).