Parametrize line segments from $0$ to $ \sqrt{3} + i $

Question

How to parametrize a line from $0$ to $ \sqrt{3} + i $ ? it's already in the form $z = x+ iy$ and I have no idea what should be done in order to integrate it for the next part. Help please

Is it supposed to be a straight line or any possible path? – Jared Apr 08 '16 at 03:14 — Jared, Apr 08 '16 at 03:14

score 1 · Answer 1 · answered Apr 08 '16 at 02:59

1

I believe it's always easier to think of $\Bbb R^2$ instead of $\Bbb C$, there you have the parametrization $(\sqrt 3 t,t), 0\le t \le 1$.

Can you adapt it?

answered Apr 08 '16 at 02:59

YoTengoUnLCD

13,384

score 0 · Answer 2 · answered Apr 08 '16 at 02:56

0

Hint: Let $\sqrt 3 + i = \rho e^{i\phi}$. Then $z = te^{i\phi}, t \in [0,\rho]$ is a possible parametrisation.

answered Apr 08 '16 at 02:56

Henricus V.

18,694

@T.Bongers It is something I've learned from http://math.stackexchange.com/questions/1585960/improper-integral-of-log-x-operatornamesech-x – Henricus V. Apr 08 '16 at 02:59

Parametrize line segments from $0$ to $ \sqrt{3} + i $

2 Answers2