If z complex number satisfying `|z-1| = 1`, then which of the following is correct

If z is any complex number satisfying |z-1|=1 , then which of the following correct?

Let s be the set of all complex numbers Z satisfying |z^(2)+z+1|=1 . Then which of the following statements is/are TRUE?

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

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

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

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

The complex number z satisfying z+|z|=1+7i then |z|^(2)=