If for a complex number `z=x+iy, sec^-1 (frac{z-2}{i})` is a real angle in `(0,frac{pi}{2}),(x,y in R)`,then

Find the locus of a complex number, z=x +iy , satisfying the relation |(z-3i)/(z+3i)| le sqrt(2) . Illustrate the locus of z in the Argand plane.

For a complex number z, the equation z^(2)+(p+iq)z+ r+" is "=0 has a real root (where p, q, r, s are non - zero real numbers and i^(2)-1 ), then

If z be any complex number (z!=0) then arg((z-i)/(z+i))=pi/2 represents the curve

x frac{dy}{dx} = y - xcos^2 frac{y}{x}

If az_(1)+bz_(2)+cz_(3)=0 for complex numbers z_(1),z_(2),z_(3) and real numbers a,b,c then z_(1),z_(2),z_(3) lie on a

Find the locus of the complex number z=x+iy , satisfying relations arg(z-1)=(pi)/(4) and |z-2-3i|=2 .

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

Fill in the blanks. If z_(1) " and " z_(2) are complex numbers such that z_(1) +z_(2) is a real number, then z_(1) = ….

Let z=1+ai be a complex number, a > 0 ,such that z^3 is a real number. Then the sum 1+z+z^2+...+ z^11 is equal to:

If a complex number z satisfies |z| = 1 and arg(z-1) = (2pi)/(3) , then ( omega is complex imaginary number)