Let \( A \equiv z_{1} ; B \equiv z_{2} ; C \equiv z_{3} \) are three complex numbers denoting th... VIDEO
Let \( A \equiv z_{1} ; B \equiv z_{2} ; C \equiv z_{3} \) are three complex numbers denoting the vertices of an acute angled triangle. If the origin \( O \) is the orthocentre of the triangle, then prove that
\[
z_{1} \bar{z}_{2}+\bar{z}_{1} z_{2}=z_{2} \bar{z}_{3}+\bar{z}_{2} z_{3}=z_{3} \bar{z}_{1}+\bar{z}_{3} z_{1}
\]
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