If $$z=x+iy$$ satisfies the condition $$|z+1|=1$$, then $$z$$ lies on the

If $$\omega$$ is the complex cube root of unity, then $$\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2\right)^2=$$

If $$x=1+2 i$$, then the value of $$x^3+7 x^2-x+16$$ is

If $$z(2-i)=(3+i)$$, then $$z^{38}=$$, ( where $$z=x+i y$$)