If complex number `z(z!=2)` satisfies the equation `z^2=4z+|z|^2+(16)/(|z|^3)` ,then the value of `|z|^4` is______.

Let z be a complex number satisfying the equation (z^3+3)^2=-16 , then find the value of |z|dot

If | z - (3)/(z) | = 2, then the least value of |z| is

A complex number z satisfies the equation |Z^(2)-9|+|Z^(2)|=41 , then the true statements among the following are

Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)

The complex number z satisfies z+|z|=2+8i . find the value of |z|-8

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

Let z be a complex number satisfying |z+16|=4|z+1| . Then

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.