query: Prove this equality using a complex polynomial lower bound
positive_passages.docid: 15886
positive_passages.text: Proof that $\frac {1} {2\pi i} \oint \frac {{\rm d}z} {P(z)} $ over a closed curve is zero.
negative_passages.docid: 57670
negative_passages.text: Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
negative_passages.docid: 57368
negative_passages.text: Prove that a positive polynomial function can be written as the squares of two polynomial functions
negative_passages.docid: 94119
negative_passages.text: Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
negative_passages.docid: 79425
negative_passages.text: Prove the direct product of nonzero complex numbers under multiplication.
negative_passages.docid: 76694
negative_passages.text: Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
negative_passages.docid: 104498
negative_passages.text: Show that $x^3y^3(x^3+y^3) \leq 2$
negative_passages.docid: 116206
negative_passages.text: Complex number question on proving an inequality.
negative_passages.docid: 114777
negative_passages.text: Using Rouché's theorem to bound zeroes of partial sums of $e^z$
negative_passages.docid: 36444
negative_passages.text: Bound of a complex-valued function
negative_passages.docid: 14836
negative_passages.text: A polynomial sequence
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 145152
negative_passages.text: How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
negative_passages.docid: 27356
negative_passages.text: Lower bound on proof length
negative_passages.docid: 77026
negative_passages.text: Proof with inequalities
negative_passages.docid: 24221
negative_passages.text: Complex numbers - minimum value proof
negative_passages.docid: 90343
negative_passages.text: Proving the inequality $|e^z-1|\leq e^{|z|}-1$