User:Mjr162006/Math

On this page I'll put some math formulas up that I found this one.


 * Complex Argument I looked everywhere for this. No one was smart enough to come up with one. That is, no one but me.

$$\arg{(a + b i)} = 4 \arctan \left (\frac{\sqrt{a^2 + b^2} - a}{b + \sqrt{2 (a^2 + b^2) - 2 a \sqrt{a^2 + b^2}}} \right)$$ This formula selects the branch of the complex argument so that the value is positive for all complex values. I derived this formula from the half-angle identity for the tangent function. I used that along with the half-angle identities for the sine and cosine to come up with this formula. This formula really helped me in high school. I derived this formula in the spring of 2007. Credit goes to me. Aside from that, go ahead and use it. I don't care were you put it, so long as you credit me. I want people to use it But I still want them to know that it was me that came up with this formula.

Note: I still have the document were I originally derived this formula. It is detailed and shows exactly how I came about this formula.

Here is a cool one.

$$a = \sum_{k=1}^\infin \frac{1}{k^{2} + k^{4}} $$

The answer.

$$a={\frac{1}{6}}{(3 + \pi^{2} - {3} {\pi} {\coth{(\pi)}})}$$