The complex numbers z_1, z_2, z_3 are the ver | vedclass

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(D) Let $A, B, C$ be the points represented by the complex numbers $z_1, z_2, z_3$ and $P$ be the point represented by $z$. For the four points $A, B,

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All the above

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(D) Let $A, B, C$ be the points represented by the complex numbers $z_1, z_2, z_3$ and $P$ be the point represented by $z$. For the four points $A, B, C, P$ to form a parallelogram,the point $P$ can be placed in three possible positions relative to the triangle $ABC$: $(i)$ If $A, B, P, C$ form a parallelogram,then $\overrightarrow{AB} = \overrightarrow{CP}$,which implies $z_2 - z_1 = z - z_3$,so $z = z_2 + z_3 - z_1$. $(ii)$ If $B, C, P, A$ form a parallelogram,then $\overrightarrow{BC} = \overrightarrow{AP}$,which implies $z_3 - z_2 = z - z_1$,so $z = z_3 + z_1 - z_2$. $(iii)$ If $C, A, P, B$ form a parallelogram,then $\overrightarrow{CA} = \overrightarrow{BP}$,which implies $z_1 - z_3 = z - z_2$,so $z = z_1 + z_2 - z_3$. Thus,all the given expressions for $z$ are correct.

The complex numbers $z_1, z_2, z_3$ are the vertices of a triangle. Then the complex numbers $z$ which make the triangle into a parallelogram are

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