Intereting Posts

The Hausdorff property versus closedness of the diagonal in the context of convergence spaces
Finding the general solution of a second order PDE
Continuous functions on discrete product topology
Using Hahn-Banach in proving result about operators and their adjoints on Banach Spaces
For $T\in \mathcal L(V)$, we have $\text{adj}(T)T=(\det T)I$.
Show that, for $t>0$, $\log t$ is not a polynomial.
Who is a Math Historian?
A question about finding a countable collection of open sets where intersection equal to S
Are continuous self-bijections of connected spaces homeomorphisms?
Maximum of $E$ for $Z$ standard normal and $X$ independent of $Z$, two-valued, with $E=c$
How to formulate continuum hypothesis without the axiom of choice?
Right adjoints preserve limits
Showing that $X^2$ and $X^3$ are irreducible but not prime in $K$
Comparison Statement
$W_n = \frac{1}{n}\sum\log(X_i) – \log(X_{(1)})$ with Delta method

The set $$\{z\in\Bbb C:1<|2z-6|\le 2\}$$

and the set $$\{z\in\Bbb C:|z|=|\Re(z)|+|\Im(z)|\}$$

- Schwarz Lemma of Complex Analysis
- Higher dimensional analogues of the argument principle?
- Radius of convergence for the exponential function
- Generalization of the argument principle
- A naive example of discrete Fourier transformation
- Laurent Series for $\cot(\pi z)$
- Condition for meromorphic to imply rational
- Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
- How to express $z^8 − 1$ as the product of two linear factors and three quadratic factors
- Limit point of sequence vs limit point of the set containing all point of the sequence

Your first step should be work out what the sets look like. I’ll leave the first one to you and get you a good start on the second one.

If $z=x+iy$, then $|z|=\sqrt{x^2+y^2}$, $|\Re(z)|=|x|$, and $|\Im(z)|=|y|$, so

$$\{z\in\Bbb C:|z|=|\Re(z)|+|\Im(z)|\}=\left\{x+iy\in\Bbb C:\sqrt{x^2+y^2}=|x|+|y|\right\}\;.$$

The defining equation on the righthand side can be squared to give $x^2+y^2=\left(|x|+|y|\right)^2$, or, after multiplying out, $x^2+y^2=x^2+2|xy|+y^2$; it should be an easy matter to use this to see what the set actually looks like, and once you’ve done that, it should be clear that the set is closed and unbounded.

- An interesting series
- Why does every countable limit ordinal have cofinality $\omega$?
- Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent?
- A “continuous monoid” is “complete”
- Conceptualizing Inclusion Map from Figure Eight to Torus
- $\alpha$ and $\beta$ are solution of $a \cdot \tan\theta + b \cdot \sec\theta = c$ show $ \tan(\alpha + \beta) = \frac{2ac}{a^2 – c^2}$
- Show that a proper continuous map from $X$ to locally compact $Y$ is closed
- when the sum of some fractions be $1$
- Problem understanding the Axiom of Foundation
- Proving the inequality $4\ge a^2b+b^2c+c^2a+abc$
- Longest increasing subsequence part II
- How to interpret “computable real numbers are not countable, and are complete”?
- Maximum area of a isosceles triangle in a circle with a radius r
- Describing the ideals for which $\operatorname{dim}_F(F/I) = 4$
- Proving that $n|m\implies f_n|f_m$