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If z₁, z₂and z₃ are the vertices of an isosceles right angled triangle, right angled at the vertex z₂, then (z₁ – z₂)² + (z₃ – z₂)² equals

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Detailed Solution

we know that $\frac{z_{3} - z_{2}}{z_{1} - z_{2}} = \frac{|z_{3} - z_{2}|}{|z_{1} - z_{2}|} \cdot e^{\frac{iπ}{2}}$
$\Rightarrow z_{3} - z_{2} = - i (z_{1} - z_{2}) \Rightarrow {(z_{3} - z_{2})}^{2} + {(z_{1} - z_{2})}^{2} = 0$

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