The complex numbers `z=x+iy` which satisfy the equation `|(z-5i)/(z+5i)|=1` lie on (a) The x-axis (b) The straight line `y=5` (c) A circle passing through the origin (d) Non of these

The complex number z which satisfies the condition |(i+z)/(i-z)| = 1 lies on

All complex numbers 'z' which satisfy the relation |z-|z+1||=|z+|z-1|| on the complex plane lie on the

Find the number of complex numbers which satisfies both the equations |z-1-i|=sqrt(2)a n d|z+1+i|=2.

If z is complex number, then the locus of z satisfying the condition |2z-1|=|z-1| is (a)perpendicular bisector of line segment joining 1/2 and 1 (b)circle (c)parabola (d)none of the above curves

If z_1, z_2, z_3 are complex numbers such that (2//z_1)=(1//z_2)+(1//z_3), then show that the points represented by z_1, z_2()_, z_3 lie on a circle passing through the origin.

If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight line c. a pair of straight line d. none of these

Variable complex number z satisfies the equation |z-1+2i|+|z+3-i|=10 . Prove that locus of complex number z is ellipse. Also, find the centre, foci and eccentricity of the ellipse.

The equation of a straight line passing through (5, 7) and is parallel to y-axis is ___.

If z = x + iy is a complex number such that |(z-4i)/(z+ 4i)| = 1 show that the locus of z is real axis.

Find the distance of the point (5,-5, -10) from the point of intersection of a straight line passing through the points A(4, 1, 2) and B(7, 5, 4) with the plane x-y+z=5.