To analyse $f:\mathbb{C} \rightarrow \mathbb{C}$ can I just analyse $f:\mathbb{R}^2 \rightarrow \mathbb{R}^2 $?
46365
Single variable complex analysis vs the world of the functions $f:\Bbb R^2 \to \Bbb R^2$.
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
145104
$T:$ $\mathbb{C}$ $\to$ $\mathbb{C}$ by $T(z)=\lambda z + \mu \bar{z}$ for every $z \in \mathbb{C}$
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement
145173
$f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
57967
Difference between $\mathbb C$ and $\mathbb R^2$
109159
What's the intuition behind $(\exists y)(\mathscr{C}(y)\supset\mathscr{D})\supset((\forall x)\mathscr{C}(x)\supset\mathscr{D})$
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
136056
$ f:\mathbb C\rightarrow \mathbb C$ defined by $f(z)=0$, if $Re(z)=0$ or $Im(z)=0$ and $f(z)=z$, otherwise.
79307
How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?
42218
How to find out the following function f which is a function of r?
83080
Question regarding $f(n)=\cot^2\left(\frac\pi n\right)+\cot^2\left(\frac{2\pi}n\right)+\cdots+\cot^2\left(\frac{(n-1)\pi}n\right)$
20955
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
121886
Proving image of $f:D^n\rightarrow \mathbb{R}^n \;$ contains $\;D^n$
123432
If $f: \mathbb{C} \to \mathbb{C}$ is continuous and analytic off $[-1,1]$ then is entire.
141115
$f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$