If z_1, z_2, z_3 are vertices of a triangle i | vedclass

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(C) Let the triangle be $	riangle Z_1 Z_2 Z_3$. Given $|z_1 - z_2| = |z_1 - z_3|$,the triangle is isosceles with $Z_1 Z_2 = Z_1 Z_3$.Let $M$ be the m

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$\pm \frac{\pi}{2}$

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(C) Let the triangle be $	riangle Z_1 Z_2 Z_3$. Given $|z_1 - z_2| = |z_1 - z_3|$,the triangle is isosceles with $Z_1 Z_2 = Z_1 Z_3$.Let $M$ be the midpoint of the base $Z_2 Z_3$. The complex number representing $M$ is $z_M = \frac{z_2 + z_3}{2}$.In an isosceles triangle,the median from the vertex $Z_1$ to the base $Z_2 Z_3$ is perpendicular to the base.Thus,the vector $Z_1 - M$ is perpendicular to the vector $Z_3 - Z_2$.The complex number $z_1 - z_M = z_1 - \frac{z_2 + z_3}{2} = \frac{2z_1 - z_2 - z_3}{2}$ represents the vector from $M$ to $Z_1$.The vector $z_3 - z_2$ represents the base $Z_2 Z_3$.Since the median is perpendicular to the base,the argument of the ratio of these two complex numbers must be $\pm \frac{\pi}{2}$.Therefore,$\arg \left( \frac{2z_1 - z_2 - z_3}{z_3 - z_2} ight) = \pm \frac{\pi}{2}$.

If $z_1, z_2, z_3$ are vertices of a triangle in the Argand plane such that $|z_1 - z_2| = |z_1 - z_3|$,then $\arg \left( \frac{2z_1 - z_2 - z_3}{z_3 - z_2} \right)$ is:

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