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+3i|+|z-i|=8 , then the locus of z, in the Argand plane, is

The locus of the point z is the Argand plane for which |z +1|^(2) + |z-1|^(2)= 4 is a

If z_(1), z_(2) and z_(3) are the vertices of a triangle in the argand plane such that |z_(1)-z_(2)|=|z_(1)-z_(3)| , then |arg((2z_(1)-z_(2)-z_(3))/(z_(3)-z_(2)))| is

Let z_(1) and z_(2) be the roots of the equation z^(2)+pz+q=0 . Suppose z_(1) and z_(2) are represented by points A and B in the Argand plane such that angleAOB=alpha , where O is the origin. Statement-1: If OA=OB, then p^(2)=4q cos^(2)alpha/2 Statement-2: If affix of a point P in the Argand plane is z, then ze^(ia) is represented by a point Q such that anglePOQ =alpha and OP=OQ .

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then prove that z_1, z_2, z_3, z_4 are concyclic.

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

If A(z_(1)) and B(z_(2)) are two points in the Argand plane such that z_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0 , then triangleOAB , is

If |z-1| =1 and arg (z)=theta , where z ne 0 and theta is acute, then (1-2/z) is equal to

If arg(z-1)=arg(z+2i) , then find (x-1):y , where z=x+iy