How is $\frac{du}{dz}=\frac{1}{2}\left(\frac{du}{dx}-i\frac{du}{dy}\right)$ and $\frac{du}{d\bar{z}}=\frac{1}{2}(\frac{du}{dx} + i\frac{du}{dy})$
107572
How does the derivative with respect to the complex conjugate even make sense?
93539
Why is $M\frac{dv}{dt} = v_{rel} .\frac{dm}{dt}$ correct and $(M - dm)\frac{dv}{dt} = v_{rel} .\frac{dm}{dt}$ wrong?
71796
Proving $\rm \frac i 2 \ln\frac {x+i}{x-i}=\arctan x$ .
76840
How to show that the modulus of $\frac{z-w}{1-\bar{z}w}$ is always $1$?
43430
What exactly does $\frac{dx}{dy}$ mean?
76441
Max. and Min. value of $|z|$ in $\left|z+\frac{2}{z}\right| = 2\,$
152895
What is wrong with this derivation of $\frac{d}{dx}x^2$?
94479
What is the center of $D_{2n}/Z(D_{2n})$
125061
Bessel function equation with derivation: $\frac{d}{dx} (xJ_{\alpha}(x)J_{\alpha+1}(x)) = x(J_{\alpha}^2(x)-J_{\alpha +1}^2(x))$
9535
Why $f(z)=\frac{az+b}{cz+d}$, $a,b,c,d \in \mathbb C$, is a linear transformation?
129605
$ 2g(z)=g(\frac{z}{2}) + g(\frac{z+1}{2})$
95265
Why is it legitimate to solve the differential equation $\frac{dy}{dx}=\frac{y}{x}$ by taking $\int \frac{1}{y}\ dy=\int \frac{1}{x}\ dx$?
83557
$\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y} \ge \frac{1}{2}(x+y+z)$
101491
If $\frac{a}{|z_2-z_3|}=\frac{b}{|z_3-z_1|}=\frac{c}{|z_1-z_2|}$, then why is $\frac{a^2}{z_2-z_3}+\frac{b^2}{z_3-z_1}+\frac{c^2}{z_1-z_2}=0$?
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
71708
Proving that $\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2$
71802
$x + \frac1y = y + \frac1z = z + \frac1x$, then value of $xyz$ is?