Among the complex numbers z which satisfies `|z-25i|<=15`, find the complex numbers z having least positive argument.

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

The complex number z satisfies thc condition |z-25/z|=24 . The maximum distance from the origin of co-ordinates to the points z is

For every real number c ge 0, find all complex numbers z which satisfy the equation abs(z)^(2)-2iz+2c(1+i)=0 , where i=sqrt(-1) and passing through (-1,4).

If |z|=2, the points representing the complex numbers -1+5z will lie on

If the complex number z is to satisfy abs(z)=3, abs(z-{a(1+i)-i}) le 3 and abs(z+2a-(a+1)i) gt 3 , where i=sqrt(-1) simultaneously for atleast one z, then find all a in R .

If a,b and c are complex numbers and z satisfies az^(2)+bz+c=0 , prove that abs(a)abs(b)=sqrt(a(bar(b))^(2)c) and abs(a)=abs(c) Leftrightarrow abs(z)=1 .

Show that the complex number z, satisfying the condition arg((z-1)/(z+1))=(pi)/(4) lie son a circle.

Consider two complex number z and omega satisfying |z|= 1 and |omega-2|+|omega-4|=2 . Then which of the following statements(s) is (are) correct?

Find argument of the complex numbers z = sqrt3 + i

Number of complex numbers satisfying z^3 = barz is