Solving ODE Problems with e^{2s} + 2e^s +2 = 0

[tandoorichicken]

ODE-related problems

How do I find all the solutions of
$$e^{2s} + 2e^s +2 = 0$$
?

 

[whozum]

That looks like a regular polynomial to me. Replace $e^{s}~with~x$ and see if you can pick it up.

 

[tandoorichicken]

okay thanks, i got that.

This is the last part of a problem for which i completed all the other parts. The question asks to find $\lambda + wi$ such that a given $z = e^{\lambda + wi}$.
For example, given $z = 1-i$, |z| = $\sqrt{2}$, arg(z) = -pi/4, so $\lambda + wi = \ln{\sqrt{2}} - \frac{\pi}{4}$

The last part of the problem asks for the same information, except with z = -2i. I have found |z| = 2, arg(z) = -1, but I can't find out what $\lambda + wi$ is supposed to be.