If `|z-iRe(z)|=|z-Im(z)|,` then prove that z
lies on the bisectors of the quadrants, `" where "i=sqrt(-1).`

Prove that |z|=|-z|

If |z^2-1|=|z|^2+1 , then z lies on :

Prove that : z= bar(z) iff z is real.

If iz^3+z^2-z+i = 0 , then show that |z|=1.

If w= z/(z-i1/3) and |w|=1,then z lies on:

Given that |z-1|=1, where z is a point on the argand planne , show that (z-2)/(z)=itan (arg z), 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).

The equation z^(2)-i|z-1|^(2)=0, where i=sqrt(-1), has.

The centre of a square ABCD is at z=0, A is z_(1) . Then, the centroid of /_\ABC is (where, i=sqrt(-1) )

Find the gratest and the least values of |z_(1)+z_(2)|, if z_(1)=24+7iand |z_(2)|=6," where "i=sqrt(-1)