Is my parametrisation correct?

Question

Find a parametrisation $f\ : \ [a,b] \rightarrow \mathbb{C}$ for the line segment from i to 1 + i.

So my answer is $f : [0,1] \rightarrow \mathbb{C}$ defined as follows f(t) = (1 - t)i + t(1 + i)

Answer 1

Yes, the parametrization is correct. In a more general setting, the line segment between $z_1,z_2 \in \Bbb C$ is parametrized by $z(t) = z_1 + t(z_2 - z_1)$, with $t \in \left[0,1\right]$. You can check that your parametrization is the same as the one I gave here, with $z_1 = i$ and $z_2 = 1+i$.