If `R e ((z-8i)/(z+6))=0` then prove that z lies on circle.

If |z+ bar(z)|+ |z-bar(z)| =2 , then z lies on

If z = ( 7-i)/(3-4i) , " then " z^(14) is equal to :

Suppose z = x + iy and w = (1-iz)/(z-i) Find absw . If absw = 1, prove that z is purely real

If the complex numbers z _(1) , z _(2) and z _(3) denote the vertices of an isosceles triangle, right angled at z _(1), then (z _(1) - z _(2)) ^(2) + (z _(1) - z _(3)) ^(2) is equal to A)0 B) (z _(2) + z _(3)) ^(2) C)2 D)3

If 3^rd , 8^th and 13^th th terms of a GP are x,y,z respectively, prove that x, y, z in GP.

If z = (2-i)/(i) , then R e(z^(2)) + I m(z^(2)) is equal to a)1 b)-1 c)2 d)-2

Let z=x+iy be a complex number such that |z+i|=2 . Then the locus of z is a circle whose centre and radius are

If the complex numbers z_1 , z_2, z_3 and z_4 denote the vertices of a square taken in order. If z_1 = 3+4i and z_3 = 5+ 6i , then the other two vertices z_2 and z_4 are respectively a) 5+4i, 5+6i b) 5+4i, 3+6i c) 5+6i, 3+5i d) 3+6i, 5+3i