ComplexNumber
On the complex plane, $z_1$ moves along the segment defined by $1+i$ and $1-i$. $z_2$ moves along the unit circle whose center is at the origin.
1) Find the trajectory of $z_1^2$
2) Find the area that is defined $z_1z_2$
3) Find the area that is defined by $z_1+z_2$