Let the complex numbers \( z_{1}, z_{2} \) and \( z_{3} \) be the v...

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Let the complex numbers \( z_{1}, z_{2} \) and \( z_{3} \) be the vertices of
\( \mathrm{P} \) an equilateral triangle. Let \( z_{0} \) be the circumcentre of the

W triangle. Then, prove that \( z_{1}^{2}+z_{2}^{2}+z_{3}^{2}=3 z_{0}^{2} \). \( (1981,4 \mathrm{M}) \)
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