970 views

### Prove $e^{i \pi} = -1$ [duplicate]

Possible Duplicate: How to prove Euler's formula: $\exp(i t)=\cos(t)+i\sin(t)$ ? I recently heard that $e^{i \pi} = -1$. WolframAlpha confirmed this for me, however, I don't see how ...
633 views

### Intuition behind euler's formula [duplicate]

Possible Duplicate: How to prove Euler's formula: $\\exp(i t)=\\cos(t)+i\\sin(t)$ ? Hi, I've been curious for quite a long time whether it is actually possible to have an intuitive ...
181 views

### Summing up the series $a_{3k}$ where $\log(1-x+x^2) = \sum a_k x^k$
If $\ln(1-x+x^2) = a_1x+a_2x^2 + \cdots \text{ then } a_3+a_6+a_9+a_{12} + \cdots =$ ? My approach is to write $1-x+x^2 = \frac{1+x^3}{1+x}$ then expanding the respective logarithms,I got a series ...
What is the logic/thinking process behind deriving an expression for even and odd functions in terms of $f(x)$ and $f(-x)$? I've been pondering about it for a few hours now, and I'm still not sure ...