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Answer by Stéphane Jaouen for $\mathcal M = \{z \in \mathbb C | |z|=r \}$ ,...
I take $r=1$, which doesn't change the generality of the problem.Let $p,q \in \mathbb R$ such that $e^{i p}=u\neq v=e^{iq}$$$u+v\color{red}{\textbf=}2\cos(\frac{p-q}2)e^{i\frac{p+q}2}\in \mathcal...
View ArticleAnswer by Vinay Karthik for $\mathcal M = \{z \in \mathbb C | |z|=r \}$ ,...
The key idea is to use the position vectors of the points on the circle.2 vectors with magnitude $r$ will add up to a vector with magnitude $r$ iff the angle between the vectors is 120°.So the angle...
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$\mathcal M = \{z \in \mathbb C | |z|=r \}$ , where $r \in \mathbb R , r >0$
The statement of the problem : Consider the set $\mathcal M = \{ z \in \mathbb C | |z|=r\} $ , where $r \in \mathbb R , r >0$a) Prove that there exists $a,b \in \mathcal M,a \neq b$ such that $a+b...
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