query: A problem involving complex numbers and polynomials to prove that $f(z) + f(−z) = 0$ for all $z ∈ C$.
positive_passages.docid: 149328
positive_passages.text: A function such that $f:\mathbb C \to \mathbb C$ such that $f(z)f(iz)=z^2$ satisfies $f(z)+f(-z)=0$.(MADHAVA-2020)
negative_passages.docid: 138329
negative_passages.text: Complex Analysis analytic function problem
negative_passages.docid: 120774
negative_passages.text: Show that $f$ has exactly one zero on the square $Q =$ {$x + iy ∈ \Bbb C : |x| < 1, |y| < 1$}.
negative_passages.docid: 111076
negative_passages.text: If $f$ is non-constant and entire, prove that there exists a $z_0 \in C$ such that $f(z_0)$ is a positive real number
negative_passages.docid: 6722
negative_passages.text: to show $f$ is a polynomial in $z$
negative_passages.docid: 158524
negative_passages.text: Complex numbers $z$ such that $|z|= 1$
negative_passages.docid: 35556
negative_passages.text: $f(z)=\frac{z}{1+|z|} $ Is 1-1?
negative_passages.docid: 108244
negative_passages.text: Proof without solving equation that if $(1+z)^n = (1-z)^n$ then Re(z) = 0. Did I do it right?
negative_passages.docid: 63255
negative_passages.text: Proving an entire, complex function with below bounded modulus is constant.
negative_passages.docid: 76311
negative_passages.text: $f'' + f =0$: finding $f$ using power series
negative_passages.docid: 76285
negative_passages.text: Suppose $f$ is entire and $|f(z)| \leq 1/|Re z|^2$ for all $z$. Show that $f $ is identically $0$.
negative_passages.docid: 114822
negative_passages.text: Prove or disprove an inequality involving complex numbers
negative_passages.docid: 74051
negative_passages.text: No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
negative_passages.docid: 35889
negative_passages.text: Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
negative_passages.docid: 154507
negative_passages.text: If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
negative_passages.docid: 15237
negative_passages.text: Prove an inequality using complex analysis
negative_passages.docid: 38568
negative_passages.text: Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.