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Rotation Concept

If z1, z2, ...

Question

If $z_{1}, z_{2}, z_{3}$ are the vertices of an isosceles triangle with right angle at $z_{2}$ , then the value of $(z_{1} - z_{2})^{2} + (z_{2} - z_{3})^{2}$ is

0

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Solution

The correct option is A $0$
$\Rightarrow (z_{1} - z_{2}) = | z_{1} - z_{2} | e^{ι θ_{1}}$
$\Rightarrow (z_{2} - z_{3}) = | z_{2} - z_{3} | e^{ι θ_{2}}$
$\Rightarrow \frac{z_{1} - z_{2}}{z_{2} - z_{3}} = e^{ι \frac{π}{2}} = ι$
$\Rightarrow {(z_{1} - z_{2})}^{2} + {(z_{2} - z_{3})}^{2} = 0$

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Similar questions

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z_{1}, z_{2}, z_{3} \in

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