### Questions (29)

 3 How to prove that $x\cdot y\neq 0$ when $x\neq 0$ and $y\neq0$ via field axioms? 3 How to prove $\big | e^{it}-1 \big |=2 \bigg |\sin \left(\frac{t}{2}\right) \bigg |$ [duplicate] 2 Proof by induction: $\sum_{j=1}^{n-1}{j^k}<\frac{n^{k+1}}{k+1}$ with $n,k \in \mathbb{N}$ and $n\geq 2$ 2 Is $\sum_{j=1}^{5}j^k=1^k+2^k+3^k+4^k+5^k$? 1 Let $z_1,z_2,z_3 \in \mathbb{C}$ with $z_i=1$ for $i=1,2,3$ and $z_1+z_2+z_3$. Show that $z_i$ are vertices for a equilateral triangle. [duplicate]

### Reputation (109)

 +15 How to prove $\big | e^{it}-1 \big |=2 \bigg |\sin \left(\frac{t}{2}\right) \bigg |$ +8 Let $z_1,z_2,z_3 \in \mathbb{C}$ with $z_i=1$ for $i=1,2,3$ and $z_1+z_2+z_3$. Show that $z_i$ are vertices for a equilateral triangle. +5 Proof that $\bigcap_{n\in\mathbb{N}}[a_n,b_n]$ is a non-emtpy set -2 Prove: If $z\in \mathbb{C}$ and $|z|=1$, then $|z+1|^2+|z-1|^2=4$.

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 0 real-analysis × 11 0 sequences-and-series × 3 0 proof-verification × 9 0 proof-explanation × 3 0 functions × 6 0 field-theory × 3 0 algebra-precalculus × 4 0 elementary-set-theory × 3 0 induction × 4 0 analysis × 2

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