If `|z^2-1|=|z|^2+1`, then `z` lies on (a) The Real axis (b)The imaginary axis (c)A circle (d)An ellipse

If |z^2-1|=|z|^2+1 , then show that z lies on the imaginary axis.

If |z+barz|+|z-barz|=2 then z lies on (a) a straight line (b) a set of four lines (c) a circle (d) None of these

If the complex number z=x+i y satisfies the condition |z+1|=1, then z lies on (a)x axis (b) circle with centre (-1,0) and radius 1 (c)y-axis (d) none of these

If |z_1|=|z_2| and arg((z_1)/(z_2))=pi , then z_1+z_2 is equal to (a) 0 (b) purely imaginary (c) purely real (d) none of these

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

If z=x+iy and w=(1-iz)/(z-i) , then |w|=1 implies that in the complex plane (A) z lies on imaginary axis (B) z lies on real axis (C) z lies on unit circle (D) None of these

The image of a complex number z in the imaginary axis is (A) z (B) iz (C) - z (D) -i z

z_1a n dz_2 are two distinct points in an Argand plane. If a|z_1|=b|z_2|(w h e r ea ,b in R), then the point (a z_1//b z_2)+(b z_2//a z_1) is a point on the line segment [-2, 2] of the real axis line segment [-2, 2] of the imaginary axis unit circle |z|=1 the line with a rgz=tan^(-1)2

If alpha = (z - i)//(z + i) show that, when z lies above the real axis, alpha will lie within the unit circle which has centre at the origin. Find the locus of alpha as z travels on the real axis form -oo "to" + oo

If z lies on the circle I z l = 1, then 2/z lies on