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find cube root of a complex number
I am looking at the following problem and not figuring out how the book's answer is correct. The question is find the cube root of $1+i$. Step 1: con...
Apr 15, 2026
Archive: News
news
How to get better at calculus?
I'm still more or less at the beginning of my journey to become a mathematician, but I already recognized that there is a huge gap relating to my ski...
Apr 15, 2026
news
How to convert a summation into a closed form
I stumbled upon two problems that I solved in an exam a while ago; however, the only reason why I solved them was through trial and error by picking each ...
Apr 15, 2026
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Using Volume of Revolution to calculate the volume of a doughnut
I'm working through a problem at the moment and I'll walk through everything I've done so far. I hit a point where I'm stuck and I don...
Apr 15, 2026
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Problem with determining cylinder height
Here is a question that I have, but I have no idea where to do go from here. Here is the question: The vase company designs a new vase that is shaped like...
Apr 15, 2026
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Mean-Square Fourier Convergence
Let $ \left \{X_n\right \} ^{\infty}_{n=1}$ be any orthogonal (in the $L^2$ sense) set of functions. Let $$S_N(f) = \sum^{N}_{n=1} \frac{(f, X_n)}{ \left ...
Apr 15, 2026
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Perfect square all 9's
For $9, 99, 999, 9999, 99999,\dots$, except $9$, are the rest of the numbers $9$'s perfect squares? Are there other perfect squares with all $9$'...
Apr 15, 2026
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Why doesn't a limit exist if you have 0 in the denominator?
Say I want to find the limit of $f(x) = \frac{p(x)}{q(x)}$ at some 'a'. I've been told the limit doesn't exist if ever the denominator...
Apr 15, 2026
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Show that $2x^6+12x^5+30x^4+60x^3+80x^2+30x+45=0$ has no real roots
I tried solving the above question but was unable to prove it. I used Descartes rule of sign, factorisation techniques, and many other things but could no...
Apr 15, 2026
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What is the difference between independent and mutually exclusive events?
Two events are mutually exclusive if they can't both happen. Independent events are events where knowledge of the probability of one doesn't cha...
Apr 15, 2026
