poirot
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 Jan 5 comment De Moivre Theorem Multiply numerator and denominator by the complex conjugate. Jan 5 revised Analytic continuation of $z-z^2+z^3-…$ added 3 characters in body Jan 5 comment Trying to solve $\int \sqrt{\sqrt{\sqrt{x}}}\left ( x \frac{1}{x} \right )dx$ Isn't $x\frac{1}{x}=1$ ? Oh I see what you've done there now... that is not really a standard way of writing $x+x^{-1}$, but I like the creative thinking ! Jan 5 comment Finding the result of an infinite sum Basically I know that if I differentiate the first sum I will get something I recognize to have a closed form. But I don't want a closed form for the derivative... I want a closed form for the original sum, which is the integral of the derivative. So I just integrate the derivative which I have in closed form. But the integral is just equal to the original sum. I haven't actually integrated any sums at all. I have just differentiated the first sum and then integrated its closed form and set equal to the original sum. Jan 5 revised Finding the result of an infinite sum deleted 2 characters in body Jan 5 revised Finding the result of an infinite sum added 36 characters in body Jan 5 revised Finding the result of an infinite sum added 2 characters in body Jan 5 answered Finding the result of an infinite sum Jan 4 revised A graphical representation of complex numbers deleted 48 characters in body Jan 4 revised Analytic continuation of $z-z^2+z^3-…$ added 161 characters in body Jan 4 revised Analytic continuation of $z-z^2+z^3-…$ added 19 characters in body Jan 4 answered Analytic continuation of $z-z^2+z^3-…$ Dec 22 comment Reduction of $\tanh(a \tanh^{-1}(x))$ That's even better. Dec 22 comment Reduction of $\tanh(a \tanh^{-1}(x))$ For that maybe this will help: $$\tanh(a+y)=\frac{\sinh (a) \cosh (y)}{\sinh (a) \sinh (y)+\cosh (a) \cosh (y)}+\frac{\cosh (a) \sinh (y)}{\sinh (a) \sinh (y)+\cosh (a) \cosh (y)}.$$ Let $y=b\tanh^{-1}(x)$ and try to expand. Dec 18 comment Logarithm of a transcendental number As an example to hopefully clarify (or possibly get wrong further)... What about $\log y$ where $y=\pi$. Here $y$ is transcendental. I don't allow/consider rewriting as $y=e^{\log\pi}$ which is what I meant in the question. Is $\log\pi$ transcendental ? What about if $t$ is some other transcendental number which I don't allow/consider rewriting in the form $t=e^x$. Will $\log t$ always be transcendental ? Dec 17 revised Logarithm of a transcendental number added 80 characters in body Dec 17 revised Logarithm of a transcendental number added 26 characters in body Dec 17 asked Logarithm of a transcendental number Nov 30 comment Solving $\exp\bigg(\frac{2+\pi i}{4} \bigg)$ To solve an equation you need an equality sign and one unknown variable such as $x$. You probably mean simplify this expression, or similar. Wording is useful, especially in exams, as it tells you what you need to do. Took me a while to realise that many moons ago :-) Nov 28 answered Complex multiplication as rotation