How to write the equations of the path to a point in complex numbers?

Question

I am given an arbitrary point G=a+ib and A(+1 in real axis), how can I write the walk from the G to the point A?

Answer 1

If the red vector is $\color{red}{G = a+ib}$ and the blue vector is $\color{blue}{A = 1+i0 = 1}$, then the green vector can be described as $\color{green}{G - A = a+ib-(1+i0) = (a-1)+i(b-0)=(a-1)+ib}.$

Answer 2

The path could be parametrized as $$z=G+t(1-G)=a+bi+t(1-a-bi)$$ where $$0\le t\le1$$