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if the complex no `z_1 , z_2 and z_3 ` represents the vertices of an equilateral triangle such that `|z_1| = | z_2| = | z_3| ` then relation among `z_1 , z_2 and z_3 `

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To find the relation among the complex numbers \( z_1, z_2, \) and \( z_3 \) that represent the vertices of an equilateral triangle, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Problem**: We know that \( z_1, z_2, z_3 \) are the vertices of an equilateral triangle and that \( |z_1| = |z_2| = |z_3| \). This means that all three points are equidistant from the origin. 2. **Rotation Formula**: ...
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