Show that the locus formed by $z$ in the equation $z^3+iz=1$ never crosses the coordinate axes in the Argand's plane.
110507
Complex Number Locus w.r.t Coordinate Axes
14759
Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
56341
Solving complex numbers equation $z^3 = \overline{z} $
40502
The Degree of Zero Polynomial.
95774
$\frac{\partial^2 u}{\partial t^2}-c^2\frac{\partial^2u}{\partial x^2}=0\text{ implies } \frac{\partial^2 u}{\partial z \partial y}=0$
3406
Prove that $\frac{\partial x}{\partial y} \frac{\partial y}{\partial z} \frac{\partial z}{\partial x} = -1$ and verify ideal gas law
85987
Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
46309
Prove that this graph is nonplanar
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
52103
Use Stokes's Theorem to show $\oint_{C} y ~dx + z ~dy + x ~dz = \sqrt{3} \pi a^2$
51314
How to prove that a complex number is not a root of unity?
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
47266
Every affine variety in $\mathbb A^n$ consisting of finitely many points can be written as the zero locus of $n$ polynomials
73262
Prove that the equation $\tan (z)=z$ has only real roots.
143100
Identify the plane defined by $|z-2i| = 2|z+3|$
141937
Prove that the $\lim_{(x,y) \to (0,0)}h(x,y)$ Does not Exist using Polar Coordinates