general
What does it mean for a function to be holomorphic?
I am trying to wrap my head around the definition of holomorphic. Wikipedia tells me that: A holomorphic function is a complex-valued function of one or m...
Apr 20, 2026
Archive: General
general
$(1+i)^6$ in polar form $re^{i\theta}$
I used De Moivre's formula and got $$ \left(\frac{\sqrt{2}}{2}\right)^6 \times \cos\left(6 \times \frac{1}{4\pi}\right) + i\sin\left(6 \times \frac{1...
Apr 20, 2026
general
Using equations to draw out complex objects
How do people come up with equations of curves to draw out complex objects? Some popular examples would include: batman curve & PSY curve. This stacke...
Apr 20, 2026
general
Road to holomorphic dynamics.
What is the best route in order to learn holomorphic dynamics? I mean, suppose that I started with Strogatz's dynamical systems, then what is the nex...
Apr 20, 2026
general
how to compute p-value when the confidence interval is given?
Please help on this problem...This is the statement: "The immunological assay verified the presence of RuBisCO in non-treated (control) and Pb-induced lea...
Apr 20, 2026
general
Prove that $x^2 + 6x + 9$ is even iff $x$ is odd
Prove. $x^2 + 6x + 9$ is even iff $x$ is odd. I had first proved this using a contrapositive statement. However, I was told I was not making a distinction...
Apr 20, 2026
general
"Direct" proof of Bochner's theorem for integrable characteristic functions?
I'm studying Bochner's theorem: If $\phi:\mathbb{R}\to\mathbb{C}$ is a Hermitian, positive definite, uniformly continuous function such that $|\...
Apr 20, 2026
general
What are differences between Geometric, Logarithmic and Exponential Growth?
At past I have read in some ecology text that geometrical, logarithmic and exponential growths are not exactly the same thing; and there were various equa...
Apr 20, 2026
general
Homogeneous groups
Let's call a group $G$ homogeneous if for every two distinct, non-identity elements $a$ and $b$ there is an automorphism $\phi$ of $G$ such that $\ph...
Apr 20, 2026
general
How many combinations from rolling 5 identical dice?
Where, for example: (1,3,1,4,6) is considered the same outcome as (1,1,3,6,4) How many total outcomes are there? Edit 1: My hunch is that there are: 6 out...
Apr 20, 2026
