Question

Parametric representation of the line segment in the complex plane from (2, 0) to (0, 2i).

Answer 1

Wait would be it \(2-2t+2it, 0\le t \le 1\)

Answer 2

Hello, Kirby,
First of all: Which of your courses is the source of this content?
Have you experience in writing equations of lines in vector form?

The line segment from (2,0) to (0,2i) is a "directed line segment." We'd start at (2,0) and travel 'northwest' (north and west at the same time). While I haven't previously attempted to express such a direction vector in complex form, I could first introduce an analogous situation in the real plane: The vector in the real plane is <0-2,2-0>, or, after simplification, <-2,2>. The vector in the real place from the origin to starting point (2,0) is <2,0>. Thus, the parametric equation of the line segment from (2,0) to (0,2) is