If \( { }_{1}, z_{2}, z_{3} \) be three distinct complex numbers satisfying \( \left|z_{1}-1\rig... VIDEO
If \( { }_{1}, z_{2}, z_{3} \) be three distinct complex numbers satisfying \( \left|z_{1}-1\right| \) \( =\left|\mathrm{z}_{2}-1\right|=\left|\mathrm{z}_{3}-1\right| \). Let \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) be the points represented in the Argand plane correspodngin to \( z_{1}, z_{2} \) and \( z_{3} \) respectively. Prove that \( z_{1}+z_{2}+z_{3}=3 \) if and only if \( \triangle A B C \) is an equilateral triangle.https://bit.ly/YTAI_PWAP https://www.pw.live
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