If a complex number z satisfies the relation `z^2+z^(-2)=2`, then the locus of z is

If z=x+iy is a complex number satisfying |z+i/2|^2=|z-i/2|^2 , then the locus of z is

If z is a complex number satisfying the relation |z+ 1|=z+2(1+i) , then z is

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

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

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

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.

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

If z is a complex number satisfying the equation |z-(1+i)|^2=2 and omega=2/z , then the locus traced by 'omega' in the complex plane is

If z is a complex number satisfying the equation |z-(1+i)|^2=2 and omega=2/z , then the locus traced by 'omega' in the complex plane is

If z be any complex number such that |3z-2|+|3z+2|=4 , then show that locus of z is a line-segment.