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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
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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
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Jan
5
answered Finding the result of an infinite sum
Jan
4
revised A graphical representation of complex numbers
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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
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Dec
17
revised Logarithm of a transcendental number
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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