\( \omega_{1}, \omega_{2}, \ldots, \omega_{n} \) be complex numbers. A line \( L \) in the argan... VIDEO
\( \omega_{1}, \omega_{2}, \ldots, \omega_{n} \) be complex numbers. A line \( L \) in the argand plane is called a mean line for the points \( \omega_{1}, \omega_{2}, \ldots, \omega_{n} \) if \( L \) contains points (complex numbers) \( z_{1}, z_{2}, \ldots, z_{n} \) such that \( \sum_{i=1}^{n}\left(z_{i}-\omega_{i}\right)=0 \). For the numbers \( \omega_{1}=32+170 i, \omega_{2}=-7 \) \( +64 i, \omega_{3}=-9+200 i, \omega_{4}=1+27 i \) and \( \omega_{5}=-14+43 i \), there is a unique mean line with \( y \)-intercept 3 . Then the slope of this mean line is equal to
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