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

For a complex number z, the product of the real parts of the roots of the equation z^(2)-z=5-5i 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)

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

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

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

Prove that z=i^i, where i=sqrt-1, is purely real.

Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) Then ,|z| is equal to

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.