Consider a curve `|z-1| =2` and a point `z_(1) =3-i` ,then the length of tangent made from the point `z_(1)` to the curve is

Let z, and z_(1)=(a)/(1-1),z_(2)=(b)/(2+1) and z_(3)=a-ib for a,b in R. If z_(1),z_(2)=1, then the centroid of the triangle formed by the points z_(1),z_(2) and z_(3), in the argand plane is given by

Statement I Tangent drawn at the point (0, 1) to the curve y=x^(3)-3x+1 meets the curve thrice at one point only. statement II Tangent drawn at the point (1, -1) to the curve y=x^(3)-3x+1 meets the curve at one point only.

If from a point P representing the complex number z_(1) on the curve |z|=2, two tangents are drawn from P to the curve |z|=1 , meeting at points Q(z_(2)) and R(z_(3)), then :

if the point z_(1)=1+i where i=sqrt(-1) is the reflection of a point z_(2)=x+iy in the line ibar(z)-iz=5 then the point z_(2) is

The range of m for which the line z(1-mi) - bar(z) (1+mi)=0 divides two chords drawn from point z_1 = sqrt(3)+i to the curve |z|=2 in the ratio 1:2 is

If z_(1) = 2+ 3i and z_(2) = 5-3i " then " z_(1)z_(2) is

if z_(1) =2+3i and z_(2) = 1+i then find, |z_(1)+z_(2)|