- #1
Bashyboy
- 1,421
- 5
Hello everyone,
I have a rather simple question. I have the curve
##
C(t) =
\begin{cases}
1 + it & \text{if}~ 0 \le t \le 2 \\
(t-1) + 2i & \text{if }~ 2 \le t \le 3
\end{cases}
##
which is obviously formed from the two curves. This curve is regarded as an arc if the functions ##x(t)## and ##y(t)## are continuous real mappings. Clearly each individual curve has continuous real mappings. But here is my concern: what if the two curves did not coincide somewhere in the complex plane, that is, they were not joined somewhere? Would the curve ##C(t)## no longer be an arc?
I have a rather simple question. I have the curve
##
C(t) =
\begin{cases}
1 + it & \text{if}~ 0 \le t \le 2 \\
(t-1) + 2i & \text{if }~ 2 \le t \le 3
\end{cases}
##
which is obviously formed from the two curves. This curve is regarded as an arc if the functions ##x(t)## and ##y(t)## are continuous real mappings. Clearly each individual curve has continuous real mappings. But here is my concern: what if the two curves did not coincide somewhere in the complex plane, that is, they were not joined somewhere? Would the curve ##C(t)## no longer be an arc?